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Full text of "Polarization Spectroscopy: Principles, Techniques and Applications."

Polarization Spectroscopy: 
Principles, Theory, 
Techniques and Applications 

Biological Applications 



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Contents 

Articles 

Copyright @ 2009 by B ci2 x 

Permission is granted to copy, distribute and/or modify this document 
under the terms of the GNU Free Documentation License, Version 1.2 or 
any later version published by the Free Software Foundation, with no 

Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A 

copy of the license is included in ;the section entitled "GNU Free 

Documentation License". 2 

Edited by Bci2, with the contributors listed after the Common Use 

License. 3 

Spectroscopy— An Introduction 4 

Spectroscopy 4 

Fourier transform spectroscopy 1 1 

Spectroscopy Theory 15 

Quantum mechanics 15 

Quantum field theory 30 

Algebraic quantum field theory 41 

Local quantum field theory 42 

Algebraic logic 43 

Quantum logic 46 

Quantum computer 53 

Quantum chemistry 62 

Density functional theory 66 

Birefringence 73 

Polarization spectroscopy 79 

Polarized IR Spectroscopy 79 

Circular dichroism 85 

Vibrational circular dichroism 91 

Optical rotatory dispersion 101 

Raman spectroscopy 101 

Coherent anti-Stokes Raman spectroscopy 107 



Raman Microscopy 110 

Imaging spectroscopy 110 

Chemical imaging 114 

Spin polarization 121 

Polarized Neutron Spectroscopy 122 

Polarized Muon Spectroscopy 124 

Time-resolved spectroscopy 126 

Terahertz spectroscopy 127 

Applied spectroscopy 128 

Amino acids 131 

Proteins 144 

Protein structure 159 

Protein folding 167 

Protein dynamics 174 

Nucleic Acids 189 

DNA 192 

Molecular models of DNA 216 

DNA structure 224 

DNA Dynamics 232 

Interactomics 239 

References 

Article Sources and Contributors 242 

Image Sources, Licenses and Contributors 247 

Article Licenses 

License 250 



Copyright® 2009 by Bci2 



Permission is granted to copy, distribute 

and/or modify this document under the terms 

of the GNU Free Documentation License, 

Version 1.2 or any later version published 

by the Free Software Foundation, with no 

Invariant Sections, no Front-Cover Texts, 

and no Back-Cover Texts. A copy of the 

license is included in ;the section entitled 

"GNU Free Documentation License". 



Edited by Bci2, with the contributors listed 
after the Common Use License. 



Spectroscopy— An Introduction 



Spectroscopy 



Spectroscopy was originally the study of the interaction between radiation and matter as a function of wavelength 
(A). In fact, historically, spectroscopy referred to the use of visible light dispersed according to its wavelength, e.g. 
by a prism. Later the concept was expanded greatly to comprise any measurement of a quantity as a function of 
either wavelength or frequency. Thus it also can refer to a response to an alternating field or varying frequency (v). A 
further extension of the scope of the definition added energy (E) as a variable, once the very close relationship E = 
hv for photons was realized (h is the Planck constant). A plot of the response as a function of wavelength — or more 
commonly frequency — is referred to as a spectrum; see also spectral linewidth. 

Spectrometry is the spectroscopic technique used to assess the concentration or amount of a given chemical 
(atomic, molecular, or ionic) species. In this case, the instrument that performs such measurements is a spectrometer, 
spectrophotometer, or spectrograph. 

Spectroscopy/spectrometry is often used in physical and analytical chemistry for the identification of substances 
through the spectrum emitted from or absorbed by them. 

Spectroscopy/spectrometry is also heavily used in astronomy and remote sensing. Most large telescopes have 
spectrometers, which are used either to measure the chemical composition and physical properties of astronomical 
objects or to measure their velocities from the Doppler shift of their spectral lines. 

Classification of methods 
Nature of excitation measured 

The type of spectroscopy depends on the physical quantity measured. Normally, the quantity that is measured is an 
intensity, either of energy absorbed or produced. 

• Electromagnetic spectroscopy involves interactions of matter with electromagnetic radiation, such as light. 

• Electron spectroscopy involves interactions with electron beams. Auger spectroscopy involves inducing the 
Auger effect with an electron beam. In this case the measurement typically involves the kinetic energy of the 
electron as variable. 

• Acoustic spectroscopy involves the frequency of sound. 

• Dielectric spectroscopy involves the frequency of an external electrical field 

• Mechanical spectroscopy involves the frequency of an external mechanical stress, e.g. a torsion applied to a piece 
of material. 

Measurement process 

Most spectroscopic methods are differentiated as either atomic or molecular based on whether or not they apply to 
atoms or molecules. Along with that distinction, they can be classified on the nature of their interaction: 

• Absorption spectroscopy uses the range of the electromagnetic spectra in which a substance absorbs. This 
includes atomic absorption spectroscopy and various molecular techniques, such as infrared, ultraviolet-visible 
and microwave spectroscopy. 

• Emission spectroscopy uses the range of electromagnetic spectra in which a substance radiates (emits). The 
substance first must absorb energy. This energy can be from a variety of sources, which determines the name of 



Spectroscopy 

the subsequent emission, like luminescence. Molecular luminescence techniques include spectrofluorimetry. 
• Scattering spectroscopy measures the amount of light that a substance scatters at certain wavelengths, incident 
angles, and polarization angles. One of the most useful applications of light scattering spectroscopy is Raman 
spectroscopy. 

Common types 
Absorption 

Absorption spectroscopy is a technique in which the power of a beam of light measured before and after interaction 
with a sample is compared. Specific absorption techniques tend to be referred to by the wavelength of radiation 
measured such as ultraviolet, infrared or microwave absorption spectroscopy. Absorption occurs when the energy of 
the photons matches the energy difference between two states of the material. 



Fluorescence 

Fluorescence spectroscopy uses higher 
energy photons to excite a sample, 
which will then emit lower energy 
photons. This technique has become 
popular for its biochemical and 
medical applications, and can be used 
for confocal microscopy, fluorescence 
resonance energy transfer, and 
fluorescence lifetime imaging. 

X-ray 

When X-rays of sufficient frequency 
(energy) interact with a substance, 
inner shell electrons in the atom are 




Wavelength | nanometer*) 



Spectrum of light from a fluorescent lamp showing prominent mercury peaks 



excited to outer empty orbitals, or they may be removed completely, ionizing the atom. The inner shell "hole" will 
then be filled by electrons from outer orbitals. The energy available in this de-excitation process is emitted as 
radiation (fluorescence) or will remove other less-bound electrons from the atom (Auger effect). The absorption or 
emission frequencies (energies) are characteristic of the specific atom. In addition, for a specific atom small 
frequency (energy) variations occur which are characteristic of the chemical bonding. With a suitable apparatus, 
these characteristic X-ray frequencies or Auger electron energies can be measured. X-ray absorption and emission 
spectroscopy is used in chemistry and material sciences to determine elemental composition and chemical bonding. 

X-ray crystallography is a scattering process; crystalline materials scatter X-rays at well-defined angles. If the 
wavelength of the incident X-rays is known, this allows calculation of the distances between planes of atoms within 
the crystal. The intensities of the scattered X-rays give information about the atomic positions and allow the 
arrangement of the atoms within the crystal structure to be calculated. However, the X-ray light is then not dispersed 
according to its wavelength, which is set at a given value, and X-ray diffraction is thus not a spectroscopy. 



Spectroscopy 

Flame 

Liquid solution samples are aspirated into a burner or nebulizer/burner combination, desolvated, atomized, and 
sometimes excited to a higher energy electronic state. The use of a flame during analysis requires fuel and oxidant, 
typically in the form of gases. Common fuel gases used are acetylene (ethyne) or hydrogen. Common oxidant gases 
used are oxygen, air, or nitrous oxide. These methods are often capable of analyzing metallic element analytes in the 
part per million, billion, or possibly lower concentration ranges. Light detectors are needed to detect light with the 
analysis information coming from the flame. 

• Atomic Emission Spectroscopy - This method uses flame excitation; atoms are excited from the heat of the 
flame to emit light. This method commonly uses a total consumption burner with a round burning outlet. A higher 
temperature flame than atomic absorption spectroscopy (AA) is typically used to produce excitation of analyte 
atoms. Since analyte atoms are excited by the heat of the flame, no special elemental lamps to shine into the flame 
are needed. A high resolution polychromator can be used to produce an emission intensity vs. wavelength 
spectrum over a range of wavelengths showing multiple element excitation lines, meaning multiple elements can 
be detected in one run. Alternatively, a monochromator can be set at one wavelength to concentrate on analysis of 
a single element at a certain emission line. Plasma emission spectroscopy is a more modern version of this 
method. See Flame emission spectroscopy for more details. 

• Atomic absorption spectroscopy (often called AA) - This method commonly uses a pre-burner nebulizer (or 
nebulizing chamber) to create a sample mist and a slot-shaped burner which gives a longer pathlength flame. The 
temperature of the flame is low enough that the flame itself does not excite sample atoms from their ground state. 
The nebulizer and flame are used to desolvate and atomize the sample, but the excitation of the analyte atoms is 
done by the use of lamps shining through the flame at various wavelengths for each type of analyte. In AA, the 
amount of light absorbed after going through the flame determines the amount of analyte in the sample. A 
graphite furnace for heating the sample to desolvate and atomize is commonly used for greater sensitivity. The 
graphite furnace method can also analyze some solid or slurry samples. Because of its good sensitivity and 
selectivity, it is still a commonly used method of analysis for certain trace elements in aqueous (and other liquid) 
samples. 

• Atomic Fluorescence Spectroscopy - This method commonly uses a burner with a round burning outlet. The 
flame is used to solvate and atomize the sample, but a lamp shines light at a specific wavelength into the flame to 
excite the analyte atoms in the flame. The atoms of certain elements can then fluoresce emitting light in a 
different direction. The intensity of this fluorescing light is used for quantifying the amount of analyte element in 
the sample. A graphite furnace can also be used for atomic fluorescence spectroscopy. This method is not as 
commonly used as atomic absorption or plasma emission spectroscopy. 

Plasma Emission Spectroscopy In some ways similar to flame atomic emission spectroscopy, it has largely 
replaced it. 

• Direct-current plasma (DCP) 

A direct-current plasma (DCP) is created by an electrical discharge between two electrodes. A plasma support gas is 
necessary, and Ar is common. Samples can be deposited on one of the electrodes, or if conducting can make up one 
electrode. 

• Glow discharge-optical emission spectrometry (GD-OES) 

• Inductively coupled plasma-atomic emission spectrometry (ICP-AES) 

• Laser Induced Breakdown Spectroscopy (LIBS) (LIBS), also called Laser-induced plasma spectrometry (LIPS) 

• Microwave-induced plasma (MIP) 

Spark or arc (emission) spectroscopy - is used for the analysis of metallic elements in solid samples. For 
non-conductive materials, a sample is ground with graphite powder to make it conductive. In traditional arc 
spectroscopy methods, a sample of the solid was commonly ground up and destroyed during analysis. An electric arc 



Spectroscopy 

or spark is passed through the sample, heating the sample to a high temperature to excite the atoms in it. The excited 
analyte atoms glow emitting light at various wavelengths which could be detected by common spectroscopic 
methods. Since the conditions producing the arc emission typically are not controlled quantitatively, the analysis for 
the elements is qualitative. Nowadays, the spark sources with controlled discharges under an argon atmosphere allow 
that this method can be considered eminently quantitative, and its use is widely expanded worldwide through 
production control laboratories of foundries and steel mills. 

Visible 

Many atoms emit or absorb visible light. In order to obtain a fine line spectrum, the atoms must be in a gas phase. 
This means that the substance has to be vaporised. The spectrum is studied in absorption or emission. Visible 
absorption spectroscopy is often combined with UV absorption spectroscopy in UV/Vis spectroscopy. Although this 
form may be uncommon as the human eye is a similar indicator, it still proves useful when distinguishing colours. 

Ultraviolet 

All atoms absorb in the Ultraviolet (UV) region because these photons are energetic enough to excite outer electrons. 
If the frequency is high enough, photoionization takes place. UV spectroscopy is also used in quantifying protein and 
DNA concentration as well as the ratio of protein to DNA concentration in a solution. Several amino acids usually 
found in protein, such as tryptophan, absorb light in the 280 nm range and DNA absorbs light in the 260 nm range. 
For this reason, the ratio of 260/280 nm absorbance is a good general indicator of the relative purity of a solution in 
terms of these two macromolecules. Reasonable estimates of protein or DNA concentration can also be made this 
way using Beer's law. 

Infrared 

Infrared spectroscopy offers the possibility to measure different types of inter atomic bond vibrations at different 
frequencies. Especially in organic chemistry the analysis of IR absorption spectra shows what type of bonds are 
present in the sample. It is also an important method for analysing polymers and constituents like fillers, pigments 
and plasticizers. 

Near Infrared (NIR) 

The near infrared NIR range, immediately beyond the visible wavelength range, is especially important for practical 
applications because of the much greater penetration depth of NIR radiation into the sample than in the case of mid 
IR spectroscopy range. This allows also large samples to be measured in each scan by NIR spectroscopy, and is 
currently employed for many practical applications such as: rapid grain analysis, medical diagnosis 
pharmaceuticals/medicines , biotechnology, genomics analysis, proteomic analysis, interactomics research, inline 
textile monitoring, food analysis and chemical imaging/hyperspectral imaging of intact organisms , plastics, 

textiles, insect detection, forensic lab application, crime detection, various military applications, and so on. 



Spectroscopy 



Raman 



Raman spectroscopy uses the inelastic scattering of light to analyse vibrational and rotational modes of molecules. 
The resulting 'fingerprints' are an aid to analysis. 



Coherent anti-Stokes Raman spectroscopy (CARS) 



CARS is a recent technique that has high sensitivity and powerful applications for in vivo spectroscopy and 

• [5] 

imaging . 

Nuclear magnetic resonance 

Nuclear magnetic resonance spectroscopy analyzes the magnetic properties of certain atomic nuclei to determine 
different electronic local environments of hydrogen, carbon, or other atoms in an organic compound or other 
compound. This is used to help determine the structure of the compound. 

Mossbauer 

Transmission or conversion-electron (CEMS) modes of Mossbauer spectroscopy probe the properties of specific 
isotope nuclei in different atomic environments by analyzing the resonant absorption of characteristic energy 
gamma-rays known as the Mossbauer effect. 

Other types 

There are many different types of materials analysis techniques under the broad heading of "spectroscopy", utilizing 
a wide variety of different approaches to probing material properties, such as absorbance, reflection, emission, 
scattering, thermal conductivity, and refractive index. 

Acoustic spectroscopy 

Auger spectroscopy is a method used to study surfaces of materials on a micro-scale. It is often used in 

connection with electron microscopy. 

Cavity ring down spectroscopy 

Circular Dichroism spectroscopy 

Deep-level transient spectroscopy measures concentration and analyzes parameters of electrically active defects in 

semiconducting materials 

Dielectric spectroscopy 

Dual polarisation interferometry measures the real and imaginary components of the complex refractive index 

Force spectroscopy 

Fourier transform spectroscopy is an efficient method for processing spectra data obtained using interferometers. 

Nearly all infrared spectroscopy techniques (such as FTIR) and nuclear magnetic resonance (NMR) are based on 

Fourier transforms. 

Fourier transform infrared spectroscopy (FTIR) 

Hadron spectroscopy studies the energy/mass spectrum of hadrons according to spin, parity, and other particle 

properties. Baryon spectroscopy and meson spectroscopy are both types of hadron spectroscopy. 

Inelastic electron tunneling spectroscopy (IETS) uses the changes in current due to inelastic electron-vibration 

interaction at specific energies which can also measure optically forbidden transitions. 

Inelastic neutron scattering is similar to Raman spectroscopy, but uses neutrons instead of photons. 

Laser spectroscopy uses lasers and other types of coherent emission sources, such as optical parametric 

oscillators, for selective excitation of atomic or molecular species. 

• Ultra fast laser spectroscopy 



Spectroscopy 

• Mechanical spectroscopy involves interactions with macroscopic vibrations, such as phonons. An example is 
acoustic spectroscopy, involving sound waves. 

• Neutron spin echo spectroscopy measures internal dynamics in proteins and other soft matter systems 

• Nuclear magnetic resonance (NMR) 

• Photoacoustic spectroscopy measures the sound waves produced upon the absorption of radiation. 

• Photothermal spectroscopy measures heat evolved upon absorption of radiation. 

• Raman optical activity spectroscopy exploits Raman scattering and optical activity effects to reveal detailed 
information on chiral centers in molecules. 

• Terahertz spectroscopy uses wavelengths above infrared spectroscopy and below microwave or millimeter wave 
measurements. 

• Time-resolved spectroscopy is the spectroscopy of matter in situations where the properties are changing with 
time. 

• Thermal infrared spectroscopy measures thermal radiation emitted from materials and surfaces and is used to 
determine the type of bonds present in a sample as well as their lattice environment. The techniques are widely 
used by organic chemists, mineralogists, and planetary scientists. 

Background subtraction 

Background subtraction is a term typically used in spectroscopy when one explains the process of acquiring a 
background radiation level (or ambient radiation level) and then makes an algorithmic adjustment to the data to 
obtain qualitative information about any deviations from the background, even when they are an order of magnitude 
less decipherable than the background itself. 

Background subtraction can affect a number of statistical calculations (Continuum, Compton, Bremsstrahlung) 
leading to improved overall system performance. 

Applications 

ro] 

• Estimate weathered wood exposure times using Near infrared spectroscopy. 

• Cure monitoring of composites using Optical fibers 



See also 

Absorption cross section 

Applied spectroscopy 

Astronomical spectroscopy 

Atomic spectroscopy 

Nuclear magnetic resonance 

2D-FT NMRI and Spectroscopy 

2D correlation analysis 

Near infrared spectroscopy 

Coherent spectroscopy 

Cold vapour atomic fluorescence spectroscopy 

Deep-level transient spectroscopy 

EPR spectroscopy 

Gamma spectroscopy 

Kelvin probe force microscope 

Metamerism (color) 

Rigid rotor 



Spectroscopy 10 

• Rotational spectroscopy 

• Saturated spectroscopy 

• Scanning tunneling spectroscopy 

• Scattering theory 

• Spectral power distributions 

• Spectral reflectance 

• Spectrophotometry 

• Spectroscopic notation 

• Spectrum analysis 

• The Unscrambler (CAMO Software) 

• Vibrational spectroscopy 

• Vibrational circular dichroism spectroscopy 

• Robert Bunsen 

• Gustav Kirchhoff 

• Joseph von Fraunhofer 

External links 

[91 

• Spectroscopy links at the Open Directory Project 

• Amateur spectroscopy links at the Open Directory Project 

• Timeline of Spectroscopy 

• Chemometric Analysis for Spectroscopy 

ri3i 

• The Science of Spectroscopy - supported by NASA, includes OpenSpectrum, a Wiki-based learning tool for 
spectroscopy that anyone can edit 

ri4i 

• A Short Study of the Characteristics of two Lab Spectroscopes 

• NIST government spectroscopy data 

• Potentiodynamic Electrochemical Impedance Spectroscopy 

References 

[I] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. Laboratory 
Journal Europe, No. 1-2, 2007 

[2] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining 

Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004. 
[3] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High Resolution Nuclear Magnetic 

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis. , D. 

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL. 
[4] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy. 2004. 1. 

C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban, q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006) 
[5] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine., 

doi:10.1146/annurev.anchem.l.031207. 112754 AnnualReview of Analytical Chemistry, 1: 883-909. 
[6] W. Demtroder, Laser Spectroscopy, 3rd Ed. (Springer, 2003). 

[7] F. J. Duarte (Ed.), Tunable Laser Applications, 2nd Ed. (CRC, 2009) Chapter 2. (http://www.opticsjournal.com/tla.htm) 
[8] "Using NIR Spectroscopy to Predict Weathered Wood Exposure Times" (http://www.fpl.fs.fed.us/documnts/pdf2006/ 

fpl_2006_wang002.pdf). . 
[9] http://www.dmoz.Org//Science/Physics/Optics/Spectroscopy// 
[10] http://www.dmoz.Org//Science/Astronomy/Amateur/Spectroscopy// 

[II] http ://spectroscopyonline. findanaly tichem. com/spec troscopy/article/articleDetail.j sp?id=3 8 1 944& sk=&date=&pageID=8 
[12] http://www.laboratoryequipment.com/article-chemometric-analysis-for-spectroscopy.aspx 

[13] http://www.scienceofspectroscopy.info 

[14] http://ioannis.virtualcomposer2000.com/spectroscope/ 

[15] http://physics.nist.gov/Pubs/AtSpec/index.html 

[16] http://www.abc.chemistry.bsu.by/vi/ 



Fourier transform spectroscopy 



11 



Fourier transform spectroscopy 



Fourier transform spectroscopy is a measurement technique whereby spectra are collected based on measurements 
of the coherence of a radiative source, using time-domain or space-domain measurements of the electromagnetic 
radiation or other type of radiation. It can be applied to a variety of types of spectroscopy including optical 
spectroscopy, infrared spectroscopy (FT IR, FT-NIRS), Fourier transform (FT) nuclear magnetic resonance , mass 
spectrometry and electron spin resonance spectroscopy. There are several methods for measuring the temporal 
coherence of the light, including the continuous wave Michelson or Fourier transform spectrometer and the pulsed 
Fourier transform spectrograph (which is more sensitive and has a much shorter sampling time than conventional 
spectroscopic techniques, but is only applicable in a laboratory environment). 



Conceptual introduction 



Measuring an emission spectrum 

One of the most basic tasks in spectroscopy is to characterize the 
spectrum of a light source: How much light is emitted at each different 
wavelength. The most straightforward way to measure a spectrum is to 
pass the light through a monochromator, an instrument that blocks all 
of the light except the light at a certain wavelength (the un-blocked 
wavelength is set by a knob on the monochromator). Then the intensity 
of this remaining (single-wavelength) light is measured. The measured 
intensity directly indicates how much light is emitted at that 
wavelength. By varying the monochromator' s wavelength setting, the 
full spectrum can be measured. This simple scheme in fact describes 
how some spectrometers work. 







Cj 








. 










C2 ** 


A 




^X> 


aV 


J ^ 



400 500 

Wavelength / nm 



An example of a spectrum: The spectrum of light 
emitted by the blue flame of a butane torch. The 
horizontal axis is the wavelength of light, and the 
vertical axis represents how much light is emitted 
by the torch at that wavelength. 



Fourier transform spectroscopy is a less intuitive way to get the same 

information. Rather than allowing only one wavelength at a time to 

pass through to the detector, this technique lets through a beam 

containing many different wavelengths of light at once, and measures the total beam intensity. Next, the beam is 

modified to contain a different combination of wavelengths, giving a second data point. This process is repeated 

many times. Afterwards, a computer takes all this data and works backwards to infer how much light there is at each 

wavelength. 

To be more specific, between the light source and the detector, there is a certain configuration of mirrors that allows 
some wavelengths to pass through but blocks others (due to wave interference). The beam is modified for each new 
data point by moving one of the mirrors; this changes the set of wavelengths that can pass through. 

As mentioned, computer processing is required to turn the raw data (light intensity for each mirror position) into the 
desired result (light intensity for each wavelength). The processing required turns out to be a common algorithm 
called the Fourier transform (hence the name, "Fourier transform spectroscopy"). The raw data is sometimes called 
an "interferogram". 



Fourier transform spectroscopy 



12 




Measuring an absorption spectrum 

The method of Fourier transform spectroscopy can also be used for 

absorption spectroscopy. The primary example is "FTIR 

Spectroscopy", a common technique in chemistry. In general, the goal 

of absorption spectroscopy is to measure how well a sample absorbs or 

transmits light at each different wavelength. However, any technique 

for emission spectroscopy can also be used for absorption spectroscopy 

as follows: Assume you have a working spectrometer that can measure 

the spectrum of any light source shining into it (as described above). 

Shine a broadband light source into the spectrometer, then shine the 

same light source through the sample into the same spectrometer. 

Comparing the two spectra, it will be obvious which wavelengths get 

absorbed by the sample and which wavelengths can pass right through 

the sample. (More precisely, the spectrum with the sample, divided by 

the "background" spectrum without the sample, equals the fraction of light that the sample can transmit at each 

wavelength.) 

Accordingly, the technique of "Fourier transform spectroscopy" can be used both for measuring emission spectra (for 
example, the emission spectrum of a star), and absorption spectra (for example, the absorption spectrum of a glass of 
liquid). 



10720 10700 10BS0 10600 10B40 

relative Ortekocrrjn 

An interferogram from a Fourier transform 

spectrometer. The horizontal axis is the position 

of the mirror, and the vertical axis is the amount 

of light detected. This is the "raw data" which can 

be transformed into an actual spectrum. 



Continuous wave Michelson or Fourier transform spectrograph 



coherent 
light source 



The Michelson spectrograph is similar to the 

instrument used in the Michelson-Morley experiment. 

Light from the source is split into two beams by a 

half-silvered mirror, one is reflected off a fixed mirror 

and one off a moving mirror which introduces a time 

delay — the Fourier transform spectrometer is just a 

Michelson interferometer with a movable mirror. The 

beams interfere, allowing the temporal coherence of the 

light to be measured at each different time delay 

setting, effectively converting the time domain into a 

spatial coordinate. By making measurements of the 

signal at many discrete positions of the moving mirror, 

the spectrum can be reconstructed using a Fourier 

transform of the temporal coherence of the light. 

Michelson spectrographs are capable of very high 

spectral resolution observations of very bright sources. 

The Michelson or Fourier transform spectrograph was 

popular for infra-red applications at a time when 

infra-red astronomy only had single pixel detectors. 

Imaging Michelson spectrometers are a possibility, but in general have been supplanted by imaging Fabry-Perot 

instruments which are easier to construct. 




detector 



The Fourier transform spectrometer is just a Michelson 

interferometer but one of the two fully-reflecting mirrors is movable, 

allowing a variable delay (in the travel-time of the light) to be 

included in one of the beams. 



Fourier transform spectroscopy 13 

Extracting the spectrum 

The intensity as a function of the path length difference in the interferometer pand wavenumber y = 1 /\ is 

Ifa V ) = I(l>) [1 + COs(27TI>p)] , 

where 1(D) is the spectrum to be determined. Note that it is not necessary for 1(D) to be modulated by the sample 
before the interferometer. In fact, most FTIR spectrometers place the sample after the interferometer in the optical 
path. The total intensity at the detector is 

I(p) = I{p,D)dD = I(D)[l + cos(2nDp)]dD. 
Jo Jo 

This is just a Fourier cosine transform. The inverse gives us our desired result in terms of the measured quantity 

("OO 

Up) = 4 / [I(p) - \l{p = 0)] cos(27ri>p)dp. 
Jo 

Pulsed Fourier transform spectrometer 

A pulsed Fourier transform spectrometer does not employ transmittance techniques. In the most general description 
of pulsed FT spectrometry, a sample is exposed to an energizing event which causes a periodic response. The 
frequency of the periodic response, as governed by the field conditions in the spectrometer, is indicative of the 
measured properties of the analyte. 

Examples of Pulsed Fourier transform spectrometry 

In magnetic spectroscopy (EPR, NMR), an RF pulse in a strong ambient magnetic field is used as the energizing 
event. This turns the magnetic particles at an angle to the ambient field, resulting in gyration. The gyrating spins then 
induce a periodic current in a detector coil. Each spin exhibits a characteristic frequency of gyration (relative to the 
field strength) which reveals information about the analyte. 

In FT-mass spectrometry, the energizing event is the injection of the charged sample into the strong electromagnetic 
field of a cyclotron. These particles travel in circles, inducing a current in a fixed coil on one point in their circle. 
Each traveling particle exhibits a characteristic cyclotron frequency-field ratio revealing the masses in the sample. 

The Free Induction Decay 

Pulsed FT spectrometry gives the advantage of requiring a single, time-dependent measurement which can easily 
deconvolute a set of similar but distinct signals. The resulting composite signal, is called a free induction decay, 
because typically the signal will decay due to inhomogeneities in sample frequency, or simply unrecoverable loss of 
signal due to entropic loss of the property being measured. 

Fellgett Advantage 

One of the most important advantages of Fourier transform spectroscopy was shown by P.B. Fellgett, an early 
advocate of the method. The Fellgett advantage, also known as the multiplex principle, states that a multiplex 
spectrometer such as the Fourier transform spectroscopy will produce a gain of the order of the square root of m in 
the signal-to-noise ratio of the resulting spectrum, when compared with an equivalent scanning monochromator, 
where m is the number of elements comprising the resulting spectrum when the measurement noise is dominated by 
detector noise. 



Fourier transform spectroscopy 14 

Converting spectra from time domain to frequency domain 

/•oo 
I(v)e- ilj2lTt dv 
-oo 

The sum is performed over all contributing frequencies to give a signal S(t) in the time domain. 

/■oo 
s(ty" 27rt dt 
-oo 

gives non-zero value when S(t) contains a component that matches the oscillating function. 
Remember that 

e lx = cos x + i sin x 

See also 

• Applied spectroscopy 

• 2D-FT NMRI and Spectroscopy 

• Forensic chemistry 

• Forensic polymer engineering 

• nuclear magnetic resonance 

• Infra-red spectroscopy 

Further reading 

• Ellis, D.I. and Goodacre, R. (2006). "Metabolic fingerprinting in disease diagnosis: biomedical applications of 
infrared and Raman spectroscopy". The Analyst 131: 875—885. doi:10.1039/b602376m. 

External links 

T31 

• Description of how a Fourier transform spectrometer works 

• The Michelson or Fourier transform spectrograph 

• Internet Journal of Vibrational Spectroscopy - How FTIR works 

• Fourier Transform Spectroscopy Topical Meeting and Tabletop Exhibit 

References 

[1] Antoine Abragam. 1968. Principles of Nuclear Magnetic Resonance., 895 pp., Cambridge University Press: Cambridge, UK. 

[2] Peter Atkins, Julio De Paula. 2006. Physical Chemistry., 8th ed. Oxford University Press: Oxford, UK. 

[3] http://scienceworld.wolfram.com/physics/FourierTransformSpectrometer.html 

[4] http://www.astro.livjm.ac.uk/courses/phys362/notes/ 

[5] http://www.ijvs.eom/volume5/edition5/sectionl.html#Feature 

[6] http://www.osa.org/meetings/topicalmeetings/fts/default.aspx 



15 



Spectroscopy Theory 



Quantum mechanics 



Quantum mechanics (QM) is a set of scientific 
principles describing the known behavior of 
energy and matter that predominate at the atomic 
and subatomic scales. The name derives from the 
observation that some physical quantities — such 
as the energy of an electron — can be changed 
only by set amounts, or quanta, rather than being 
capable of varying by any amount. The 
wave— particle duality of energy and matter at the 
atomic scale provides a unified view of the 
behavior of particles such as photons and 
electrons. Photons are the quanta of light, and 
have energy values proportional to their 
frequency via the Planck constant. An electron 
bound in an atomic orbital has quantized values of 
angular momentum and energy. The unbound 
electron does not exhibit quantized energy levels, 
but is associated with a quantum mechanical 
wavelength, as are all massive particles. The full 
significance of the Planck constant is expressed in 
physics through the abstract mathematical notion 
of action. 



o - m—4 



Fig. 1 : Probability densities corresponding to the wavefunctions of an 
electron in a hydrogen atom possessing definite energy levels (increasing 

from the top of the image to the bottom: n = 1, 2, 3, ...) and angular 
momentum (increasing across from left to right: s, p, d,...). Brighter areas 

correspond to higher probability density in a position measurement. 
Wavefunctions like these are directly comparable to Chladni's figures of 

acoustic modes of vibration classical physics and are indeed modes of 

oscillation as well: they possess a sharp energy and thus a keen frequency. 

The angular momentum and energy are quantized, and only take on discrete 

values like those shown (as is the case for resonant frequencies in 

acoustics). 



The mathematical formulation of quantum 

mechanics is abstract and its implications are 

often non-intuitive. The centerpiece of this 

mathematical system is the wavefunction. The 

wavefunction is a mathematical function of time and space that can provide information about the position and 

momentum of a particle, but only as probabilities, as dictated by the constraints imposed by the uncertainty principle. 

Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an 

understanding of complex numbers and linear functionals. Many of the results of QM can only be expressed 

mathematically and do not have models that are as easy to visualize as those of classical mechanics. For instance, the 

ground state in quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a 

system, rather than a more traditional system that is thought of as simple being at rest with zero kinetic energy. 



Overview 

The word quantum derives from Latin meaning "how great" or "how much". In quantum mechanics, it refers to a 
discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest (see 
Figure 1). The discovery that particles are discrete packets of energy with wave-like properties led to the branch of 



Quantum mechanics 16 

physics that deals with atomic and subatomic systems which is today called quantum mechanics. It is the underlying 
mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state 
physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry, 
particle physics, nuclear chemistry, and nuclear physics. The foundations of quantum mechanics were established 
during the first half of the twentieth century by Werner Heisenberg, Max Planck, Louis de Broglie, Albert Einstein, 
Niels Bohr, Erwin Schrodinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli, David Hilbert, and 
others. Some fundamental aspects of the theory are still actively studied. 

Quantum mechanics is essential to understand the behavior of systems at atomic length scales and smaller. For 
example, if classical mechanics governed the workings of an atom, electrons would rapidly travel towards and 
collide with the nucleus, making stable atoms impossible. However, in the natural world the electrons normally 
remain in an uncertain, non-deterministic "smeared" (wave— particle wave function) orbital path around or through 
the nucleus, defying classical electromagnetism. 

Quantum mechanics was initially developed to provide a better explanation of the atom, especially the spectra of 
light emitted by different atomic species. The quantum theory of the atom was developed as an explanation for the 
electron's staying in its orbital, which could not be explained by Newton's laws of motion and by Maxwell's laws of 
classical electromagnetism. 

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave 
function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a 
complex vector space. This abstract mathematical object allows for the calculation of probabilities of outcomes of 
concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular 
region around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneous 
predictions of conjugate variables, such as position and momentum, with accuracy. For instance, electrons may be 
considered to be located somewhere within a region of space, but with their exact positions being unknown. 
Contours of constant probability, often referred to as "clouds", may be drawn around the nucleus of an atom to 
conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle 
quantifies the inability to precisely locate the particle given its conjugate. 

The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. When it 
was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or 
quanta, Albert Einstein further developed this idea to show that an electromagnetic wave such as light could be 
described by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory of 
unity between subatomic particles and electromagnetic waves called wave— particle duality in which particles and 
waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the 
world of the very small, it also is needed to explain certain macroscopic quantum systems such as superconductors 
and superfluids. 

Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot 
account: (I) the quantization (discretization) of certain physical quantities, (II) wave— particle duality, (III) the 
uncertainty principle, and (IV) quantum entanglement. Each of these phenomena is described in detail in subsequent 
sections. 

History 

The history of quantum mechanics began with the 1838 discovery of cathode rays by Michael Faraday, the 1859 
statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that 
the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by Max Planck. 
Planck's hypothesis stated that any energy is radiated and absorbed in quantities divisible by discrete "energy 
elements", such that each energy element E is proportional to its frequency v: 

E = hv 



Quantum mechanics 17 

where h is Planck's action constant. Planck insisted that this was simply an aspect of the processes of absorption and 

ro"| 

emission of radiation and had nothing to do with the physical reality of the radiation itself. However, at that time, 
this appeared not to explain the photoelectric effect (1839), i.e. that shining light on certain materials can eject 
electrons from the material. In 1905, basing his work on Planck's quantum hypothesis, Albert Einstein postulated that 
light itself consists of individual quanta. 

In the mid- 1920s, developments in quantum mechanics quickly led to it becoming the standard formulation for 
atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the "Old Quantum 
Theory". Light quanta came to be called photons (1926). From Einstein's simple postulation was born a flurry of 
debating, theorizing and testing, and thus, the entire field of quantum physics, leading to its wider acceptance at the 
Fifth Solvay Conference in 1927. 

Quantum mechanics and classical physics 

Predictions of quantum mechanics have been verified experimentally to a very high degree of accuracy. Thus, the 
current logic of correspondence principle between classical and quantum mechanics is that all objects obey laws of 
quantum mechanics, and classical mechanics is just a quantum mechanics of large systems (or a statistical quantum 
mechanics of a large collection of particles). Laws of classical mechanics thus follow from laws of quantum 
mechanics at the limit of large systems or large quantum numbers. However, chaotic systems do not have good 
quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these 
systems. 

The main differences between classical and quantum theories have already been mentioned above in the remarks on 
the Einstein-Podolsky-Rosen paradox. Essentially the difference boils down to the statement that quantum 
mechanics is coherent (addition of amplitudes), whereas classical theories are incoherent (addition of intensities). 
Thus, such quantities as coherence lengths and coherence times come into play. For microscopic bodies the 
extension of the system is certainly much smaller than the coherence length; for macroscopic bodies one expects that 
it should be the other way round. An exception to this rule can occur at extremely low temperatures, when 
quantum behavior can manifest itself on more macroscopic scales (see Bose-Einstein condensate). 

This is in accordance with the following observations: 

Many macroscopic properties of classical systems are direct consequences of quantum behavior of its parts. For 
example, the stability of bulk matter (which consists of atoms and molecules which would quickly collapse under 

electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties 

ri2i 
of matter are all results of interaction of electric charges under the rules of quantum mechanics. 

While the seemingly exotic behavior of matter posited by quantum mechanics and relativity theory become more 
apparent when dealing with extremely fast-moving or extremely tiny particles, the laws of classical Newtonian 
physics remain accurate in predicting the behavior of large objects — of the order of the size of large molecules and 

ri3i 

bigger — at velocities much smaller than the velocity of light. 



Quantum mechanics 



18 



Theory 

There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most 
commonly used formulations is the transformation theory proposed by Cambridge theoretical physicist Paul Dirac, 
which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by 
Werner Heisenberg) and wave mechanics (invented by Erwin Schrodinger). 

In this formulation, the instantaneous state of a quantum system encodes the probabilities of its measurable 
properties, or "observables". Examples of observables include energy, position, momentum, and angular momentum. 
Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron 

ri7i 

bound to a hydrogen atom). Generally, quantum mechanics does not assign definite values to observables. 
Instead, it makes predictions using probability distributions; that is, the probability of obtaining possible outcomes 
from measuring an observable. Oftentimes these results are skewed by many causes, such as dense probability 
clouds or quantum state nuclear attraction. Naturally, these probabilities will depend on the quantum state 

at the "instant" of the measurement. Hence, uncertainty is involved in the value. There are, however, certain states 

that are associated with a definite value of a particular observable. These are known as eigenstates of the observable 

1211 
("eigen" can be translated from German as inherent or as a characteristic). In the everyday world, it is natural and 

intuitive to think of everything (every observable) as being in an eigenstate. Everything appears to have a definite 

position, a definite momentum, a definite energy, and a definite time of occurrence. However, quantum mechanics 

does not pinpoint the exact values of a particle for its position and momentum (since they are conjugate pairs) or its 

energy and time (since they too are conjugate pairs); rather, it only provides a range of probabilities of where that 

particle might be given its momentum and momentum probability. Therefore, it is helpful to use different words to 

describe states having uncertain values and states having definite values (eigenstate). 

For example, consider a free particle. 

In quantum mechanics, there is 

wave-particle duality so the properties 

of the particle can be described as the 

properties of a wave. Therefore, its 

quantum state can be represented as a 

wave of arbitrary shape and extending 

over space as a wave function. The 

position and momentum of the particle 

are observables. The Uncertainty 

Principle states that both the position 

and the momentum cannot 

simultaneously be measured with full 

precision at the same time. However, 

one can measure the position alone of a 

moving free particle creating an eigenstate of position with a wavefunction that is very large (a Dirac delta) at a 

particular position x and zero everywhere else. If one performs a position measurement on such a wavefunction, the 

result x will be obtained with 100% probability (full certainty). This is called an eigenstate of position 

(mathematically more precise: a generalized position eigenstate ( eigendistribution)) . If the particle is in an eigenstate 

of position then its momentum is completely unknown. On the other hand, if the particle is in an eigenstate of 

T221 
momentum then its position is completely unknown. In an eigenstate of momentum having a plane wave form, it 

can be shown that the wavelength is equal to h/p, where h is Planck's constant and p is the momentum of the 

* * [23] 

eigenstate. 




±J 



Energy Level = #1 



D= 



Energy Level = #1 
3 00 _l[j 



■ H 



3 opti 



3D confined electron wave functions for each eigenstate in a Quantum Dot. Here, 

rectangular and triangular-shaped quantum dots are shown. Energy states in rectangular 

dots are more 's-type' and 'p-type'. However, in a triangular dot the wave functions are 

mixed due to confinement symmetry. 



Usually, a system will not be in an eigenstate of the observable we are interested in. However, if one measures the 
observable, the wavefunction will instantaneously be an eigenstate (or generalized eigenstate) of that observable. 



Quantum mechanics 19 

T241 
This process is known as wavefunction collapse, a debatable process. It involves expanding the system under 

study to include the measurement device. If one knows the corresponding wave function at the instant before the 

measurement, one will be able to compute the probability of collapsing into each of the possible eigenstates. For 

example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered 

around some mean position x , neither an eigenstate of position nor of momentum. When one measures the position 

[25] 
of the particle, it is impossible to predict with certainty the result. It is probable, but not certain, that it will be 

near x , where the amplitude of the wave function is large. After the measurement is performed, having obtained 

some result x, the wave function collapses into a position eigenstate centered at x. 

Wave functions can change as time progresses. An equation known as the Schrodinger equation describes how wave 
functions change in time, a role similar to Newton's second law in classical mechanics. The Schrodinger equation, 
applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move 
through space at a constant velocity, like a classical particle with no forces acting on it. However, the wave packet 
will also spread out as time progresses, which means that the position becomes more uncertain. This also has the 

effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave 

T271 
packets that are no longer position eigenstates. Some wave functions produce probability distributions that are 

constant or independent of time, such as when in a stationary state of constant energy, time drops out of the absolute 

square of the wave function. Many systems that are treated dynamically in classical mechanics are described by such 

"static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle 

moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, 

spherically symmetric wavefunction surrounding the nucleus (Fig. 1). (Note that only the lowest angular momentum 

rofil 

states, labeled s, are spherically symmetric). 

The time evolution of wave functions is deterministic in the sense that, given a wavefunction at an initial time, it 

[291 
makes a definite prediction of what the wavefunction will be at any later time. During a measurement, the change 

of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random. A time-evolution 

simulation can be seen here. [30] 

The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most 
difficult aspects of quantum systems to understand. It was the central topic in the famous Bohr-Einstein debates, in 
which the two scientists attempted to clarify these fundamental principles by way of thought experiments. In the 
decades after the formulation of quantum mechanics, the question of what constitutes a "measurement" has been 
extensively studied. Interpretations of quantum mechanics have been formulated to do away with the concept of 
"wavefunction collapse"; see, for example, the relative state interpretation. The basic idea is that when a quantum 
system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original 
quantum system ceases to exist as an independent entity. For details, see the article on measurement in quantum 
mechanics. 

Mathematical formulation 

T321 
In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von 

T331 
Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called "state 

vectors") residing in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert 

space" of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible 

states are points in the projectivization of a Hilbert space, usually called the complex projective space. The exact 

nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum 

states is the space of square-integrable functions, while the state space for the spin of a single proton is just the 

product of two complex planes. Each observable is represented by a maximally-Hermitian (precisely: by a 

self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector 

of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the 



Quantum mechanics 20 

operator's spectrum is discrete, the observable can only attain those discrete eigenvalues. 

The time evolution of a quantum state is described by the Schrodinger equation, in which the Hamiltonian, the 
operator corresponding to the total energy of the system, generates time evolution. 

The inner product between two state vectors is a complex number known as a probability amplitude. During a 
measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by 
the square of the absolute value of the probability amplitudes between the initial and final states. The possible results 
of a measurement are the eigenvalues of the operator — which explains the choice of Hermitian operators, for which 
all the eigenvalues are real. We can find the probability distribution of an observable in a given state by computing 
the spectral decomposition of the corresponding operator. Heisenberg's uncertainty principle is represented by the 
statement that the operators corresponding to certain observables do not commute. 

The Schrodinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the 
absolute value of the probability amplitude encodes information about probabilities, its phase encodes information 
about the interference between quantum states. This gives rise to the wave-like behavior of quantum states. 

It turns out that analytic solutions of Schrodinger's equation are only available for a small number of model 
Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen molecular ion and the 
hydrogen atom are the most important representatives. Even the helium atom, which contains just one more electron 
than hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating 
approximate solutions. For instance, in the method known as perturbation theory one uses the analytic results for a 
simple quantum mechanical model to generate results for a more complicated model related to the simple model by, 
for example, the addition of a weak potential energy. Another method is the "semi-classical equation of motion" 
approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. 
The deviations can be calculated based on the classical motion. This approach is important for the field of quantum 
chaos. 

An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a 
quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the 
quantum-mechanical counterpart of action principles in classical mechanics. 

Interactions with other scientific theories 

The fundamental rules of quantum mechanics are very deep. They assert that the state space of a system is a Hilbert 
space and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space or 
which operators, or if it even exists. These must be chosen appropriately in order to obtain a quantitative description 
of a quantum system. An important guide for making these choices is the correspondence principle, which states that 
the predictions of quantum mechanics reduce to those of classical physics when a system moves to higher energies 
or equivalently, larger quantum numbers. In other words, classical mechanics is simply a quantum mechanics of 
large systems. This "high energy" limit is known as the classical or correspondence limit. One can therefore start 
from an established classical model of a particular system, and attempt to guess the underlying quantum model that 
gives rise to the classical model in the correspondence limit. 



Quantum mechanics 21 



Unsolved problems in physics 

^Q 



In the correspondence limit of quantum mechanics: Is there a preferred interpretation of quantum mechanics? How does the quantum 
description of reality, which includes elements such as the "superposition of states" and "wavefunction collapse", give rise to the reality 
we perceive? 



When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was 
non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an 
explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the 
classical harmonic oscillator. 

Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrodinger 
equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. While these theories 
were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from 
their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the 
development of quantum field theory, which applies quantization to a field rather than a fixed set of particles. The 
first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the 
electromagnetic interaction. 

The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler 
approach, one employed since the inception of quantum mechanics, is to treat charged particles as quantum 
mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model 
of the hydrogen atom describes the electric field of the hydrogen atom using a classical —-^- — 7 Coulomb 

potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important 
role, such as in the emission of photons by charged particles. 

Quantum field theories for the strong nuclear force and the weak nuclear force have been developed. The quantum 
field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of the 
subnuclear particles: quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their 

quantized forms, into a single quantum field theory known as electroweak theory, by the physicists Abdus Salam, 

T341 
Sheldon Glashow and Steven Weinberg. These three men shared the Nobel Prize in Physics in 1979 for this work. 

It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classical 
approximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of a 
complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity, the most 
accurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. The 
resolution of these incompatibilities is an area of active research, and theories such as string theory are among the 
possible candidates for a future theory of quantum gravity. 

In the 21st century classical mechanics has been extended into the complex domain and complex classical mechanics 

T351 
exhibits behaviours very similar to quantum mechanics. 



Quantum mechanics 22 

Example 

The particle in a 1 -dimensional potential energy box is the most simple example where restraints lead to the 
quantization of energy levels. The box is defined as zero potential energy inside a certain interval and infinite 
everywhere outside that interval. For the 1 -dimensional case in the x direction, the time-independent Schrodinger 
equation can be written as: 

2m dx 2 
The general solutions are: 

T) 2 k 2 
if>(x) = Ae lkx + Be- lkx E = — — 

2m 

or, from Euler's formula, 

ip(x) — C sin kx + D cos kx. 
The presence of the walls of the box determines the values of C, D, and k. At each wall (x = and x = L), \p = 0. 
Thus when x = 0, 

^(0) =0 = CsinO + DcosO = Z) 
and so D = 0. When x = L, 

i/j(L) =0 = Csin£;L. 
C cannot be zero, since this would conflict with the Born interpretation. Therefore sin kL = 0, and so it must be that 
kL is an integer multiple of jt. Therefore, 

k = — n = 1, 2, 3, ... . 

L 
The quantization of energy levels follows from this constraint on k, since 

^ fcW n 2 h 2 
E 



2mL 2 SmL 2 ' 

Attempts at a unified field theory 

As of 2010 the quest for unifying the fundamental forces through quantum mechanics is still ongoing. Quantum 

T371 
electrodynamics (or "quantum electromagnetism"), which is currently the most accurately tested physical theory, 

has been successfully merged with the weak nuclear force into the electroweak force and work is currently being 

done to merge the electroweak and strong force into the electrostrong force. Current predictions state that at around 

10 GeV the three aforementioned forces are fused into a single unified field, Beyond this "grand unification", it 

is speculated that it may be possible to merge gravity with the other three gauge symmetries, expected to occur at 

19 
roughly 10 GeV. However — and while special relativity is parsimoniously incorporated into quantum 

electrodynamics — the expanded general relativity, currently the best theory describing the gravitation force, has not 

been fully incorporated into quantum theory. 



Quantum mechanics 23 

Relativity and quantum mechanics 

Main articles: Quantum gravity and Theory of everything 

Even with the defining postulates of both Einstein's theory of general relativity and quantum theory being 
indisputably supported by rigorous and repeated empirical evidence and while they do not directly contradict each 
other theoretically (at least with regard to primary claims), they are resistant to being incorporated within one 
cohesive model. 

Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly contributing to 
the field, he did not accept the more philosophical consequences and interpretations of quantum mechanics, such as 
the lack of deterministic causality and the assertion that a single subatomic particle can occupy numerous areas of 
space at one time. He also was the first to notice some of the apparently exotic consequences of entanglement and 
used them to formulate the Einstein-Podolsky-Rosen paradox, in the hope of showing that quantum mechanics had 
unacceptable implications. This was 1935, but in 1964 it was shown by John Bell (see Bell inequality) that Einstein's 
assumption was correct, but had to be completed by hidden variables and thus based on wrong philosophical 
assumptions. According to the paper of J. Bell and the Copenhagen interpretation (the common interpretation of 
quantum mechanics by physicists since 1927), and contrary to Einstein's ideas, quantum mechanics was 

• neither a "realistic" theory (since quantum measurements do not state pre-existing properties, but rather they 
prepare properties) 

• nor a local theory (essentially not, because the state vector \ip) determines simultaneously the probability 
amplitudes at all sites, Ujj\ — > ■j/.'fr), Vr)- 

The Einstein-Podolsky-Rosen paradox shows in any case that there exist experiments by which one can measure the 
state of one particle and instantaneously change the state of its entangled partner, although the two particles can be 
an arbitrary distance apart; however, this effect does not violate causality, since no transfer of information happens. 
These experiments are the basis of some of the most topical applications of the theory, quantum cryptography, which 
has been on the market since 2004 and works well, although at small distances of typically < 1000 km. 

Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum 
mechanics is not an urgent issue in those applications. However, the lack of a correct theory of quantum gravity is an 
important issue in cosmology and physicists' search for an elegant "theory of everything". Thus, resolving the 
inconsistencies between both theories has been a major goal of twentieth- and twenty-first-century physics. Many 
prominent physicists, including Stephen Hawking, have labored in the attempt to discover a theory underlying 
everything, combining not only different models of subatomic physics, but also deriving the universe's four 
forces — the strong force, electromagnetism, weak force, and gravity — from a single force or phenomenon. One of 
the leaders in this field is Edward Witten, a theoretical physicist who formulated the groundbreaking M-theory, 
which is an attempt at describing the supersymmetrical based string theory. 

Applications 

Quantum mechanics has had enormous success in explaining many of the features of our world. The individual 
behaviour of the subatomic particles that make up all forms of matter — electrons, protons, neutrons, photons and 
others — can often only be satisfactorily described using quantum mechanics. Quantum mechanics has strongly 
influenced string theory, a candidate for a theory of everything (see reductionism) and the multiverse hypothesis. It is 
also related to statistical mechanics. 

Quantum mechanics is important for understanding how individual atoms combine covalently to form chemicals or 
molecules. The application of quantum mechanics to chemistry is known as quantum chemistry. (Relativistic) 
quantum mechanics can in principle mathematically describe most of chemistry. Quantum mechanics can provide 
quantitative insight into ionic and covalent bonding processes by explicitly showing which molecules are 
energetically favorable to which others, and by approximately how much. Most of the calculations performed in 



Quantum mechanics 



24 



computational chemistry rely on quantum mechanics 

Much of modern technology operates 
at a scale where quantum effects are 
significant. Examples include the laser, 
the transistor (and thus the microchip), 
the electron microscope, and magnetic 
resonance imaging. The study of 
semiconductors led to the invention of 
the diode and the transistor, which are 
indispensable for modern electronics. 



[41] 



Result: iBands+Transmission+CurrentDensity+IV 



- 



0.3 ■ 



0.2 - 



oj 0.1 



- 



±J 




12 3 

Composite Plot Axis 
Bancls+Transmission+QiiTientDensity+IV = 1_Bias=0V 

El = 



J Optio 



A working mechanism of a Resonant Tunneling Diode device, based on the phenomenon 
of quantum tunneling through the potential barriers. 



Researchers are currently seeking 

robust methods of directly 

manipulating quantum states. Efforts 

are being made to develop quantum 

cryptography, which will allow 

guaranteed secure transmission of 

information. A more distant goal is the 

development of quantum computers, 

which are expected to perform certain 

computational tasks exponentially 

faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques 

to transmit quantum states over arbitrary distances. 

Quantum tunneling is vital in many devices, even in the simple light switch, as otherwise the electrons in the electric 
current could not penetrate the potential barrier made up of a layer of oxide. Flash memory chips found in USB 
drives use quantum tunneling to erase their memory cells. 

QM primarily applies to the atomic regimes of matter and energy, but some systems exhibit quantum mechanical 
effects on a large scale; superfluidity (the frictionless flow of a liquid at temperatures near absolute zero) is one 
well-known example. Quantum theory also provides accurate descriptions for many previously unexplained 
phenomena such as black body radiation and the stability of electron orbitals. It has also given insight into the 
workings of many different biological systems, including smell receptors and protein structures. Even so, 
classical physics often can be a good approximation to results otherwise obtained by quantum physics, typically in 
circumstances with large numbers of particles or large quantum numbers. (However, some open questions remain in 
the field of quantum chaos.) 



Philosophical consequences 

Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong philosophical 
debate and many interpretations. Even fundamental issues such as Max Born's basic rules concerning probability 
amplitudes and probability distributions took decades to be appreciated. 

The Copenhagen interpretation, due largely to the Danish theoretical physicist Niels Bohr, is the interpretation of 
quantum mechanics most widely accepted amongst physicists. According to it, the probabilistic nature of quantum 
mechanics predictions cannot be explained in terms of some other deterministic theory, and does not simply reflect 
our limited knowledge. Quantum mechanics provides probabilistic results because the physical universe is itself 
probabilistic rather than deterministic. 

Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement 
(this dislike is the source of his famous quote, "God does not play dice with the universe."). Einstein held that there 



Quantum mechanics 25 

should be a local hidden variable theory underlying quantum mechanics and that, consequently, the present theory 
was incomplete. He produced a series of objections to the theory, the most famous of which has become known as 
the Einstein-Podolsky-Rosen paradox. John Bell showed that the EPR paradox led to experimentally testable 
differences between quantum mechanics and local realistic theories. Experiments have been performed confirming 

the accuracy of quantum mechanics, thus demonstrating that the physical world cannot be described by local realistic 

T431 
theories. The Bohr-Einstein debates provide a vibrant critique of the Copenhagen Interpretation from an 

epistemological point of view. 

The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum 

T441 
theory simultaneously occur in a multiverse composed of mostly independent parallel universes. This is not 

accomplished by introducing some new axiom to quantum mechanics, but on the contrary by removing the axiom of 

the collapse of the wave packet: All the possible consistent states of the measured system and the measuring 

apparatus (including the observer) are present in a real physical (not just formally mathematical, as in other 

interpretations) quantum superposition. Such a superposition of consistent state combinations of different systems is 

called an entangled state. 

While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we 
can observe only the universe, i.e. the consistent state contribution to the mentioned superposition, we inhabit. 
Everett's interpretation is perfectly consistent with John Bell's experiments and makes them intuitively 
understandable. However, according to the theory of quantum decoherence, the parallel universes will never be 
accessible to us. This inaccessibility can be understood as follows: Once a measurement is done, the measured 
system becomes entangled with both the physicist who measured it and a huge number of other particles, some of 
which are photons flying away towards the other end of the universe; in order to prove that the wave function did not 
collapse one would have to bring all these particles back and measure them again, together with the system that was 
measured originally. This is completely impractical, but even if one could theoretically do this, it would destroy any 
evidence that the original measurement took place (including the physicist's memory). 

See also 

Copenhagen interpretation 

Correspondence rules 

De Broglie— Bohm theory 

EPR paradox 

Fine-structure constant 

Interpretation of quantum mechanics 

Introduction to quantum mechanics 

Many-worlds interpretation 

Measurement in quantum mechanics 

Measurement problem 

Photon dynamics in the double-slit experiment 

Photon polarization 

Physical ontology 

Quantum chaos 

Quantum chemistry 

Quantum chemistry computer programs 

Quantum chromodynamics 

Quantum computers 

Quantum decoherence 

Quantum electrochemistry 



Quantum mechanics 26 

Quantum electronics 

Quantum field theory 

Quantum information 

Quantum mind 

Quantum optics 

Quantum pseudo-telepathy 

Quantum thermodynamics 

Quantum triviality 

Quantum Zeno effect 

Quasi-set theory 

Relation between Schrodinger's equation and the path integral formulation of quantum mechanics 

Schrodinger's cat 

Theoretical and experimental justification for the Schrodinger equation 

Theoretical chemistry 

Transactional interpretation 

Trojan wave packet 

References 

The following titles, all by working physicists, attempt to communicate quantum theory to lay people, using a 
minimum of technical apparatus. 

• Chester, Marvin (1987) Primer of Quantum Mechanics. John Wiley. ISBN 0-486-42878-8 

• Richard Feynman, 1985. QED: The Strange Theory of Light and Matter, Princeton University Press. ISBN 
0-691-08388-6. Four elementary lectures on quantum electrodynamics and quantum field theory, yet containing 
many insights for the expert. 

• Ghirardi, GianCarlo, 2004. Sneaking a Look at God's Cards, Gerald Malsbary, trans. Princeton Univ. Press. The 
most technical of the works cited here. Passages using algebra, trigonometry, and bra-ket notation can be passed 
over on a first reading. 

• N. David Mermin, 1990, "Spooky actions at a distance: mysteries of the QT" in his Boojums all the way through. 
Cambridge University Press: 110-76. 

• Victor Stenger, 2000. Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Buffalo NY: Prometheus 
Books. Chpts. 5-8. Includes cosmological and philosophical considerations. 

More technical: 

• Bryce DeWitt, R. Neill Graham, eds., 1973. The Many-Worlds Interpretation of Quantum Mechanics, Princeton 
Series in Physics, Princeton University Press. ISBN 0-691-08 13 1-X 

• Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. ISBN 01985201 15. The beginning chapters make 
up a very clear and comprehensible introduction. 

• Hugh Everett, 1957, "Relative State Formulation of Quantum Mechanics," Reviews of Modern Physics 29: 
454-62. 

• Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (1965). The Feynman Lectures on Physics. 1-3. 
Addison- Wesley. ISBN 0738200085. 

• Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-1 1 1892-7. 
OCLC 40251748. A standard undergraduate text. 

• Max Jammer, 1966. The Conceptual Development of Quantum Mechanics. McGraw Hill. 

• Hagen Kleinert, 2004. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 
3rd ed. Singapore: World Scientific. Draft of 4th edition. 

• Gunther Ludwig, 1968. Wave Mechanics. London: Pergamon Press. ISBN 0-08-203204-1 



Quantum mechanics 27 

• George Mackey (2004). The mathematical foundations of quantum mechanics. Dover Publications. ISBN 
0-486-43517-2. 

• Albert Messiah, 1966. Quantum Mechanics (Vol. I), English translation from French by G. M. Temmer. North 
Holland, John Wiley & Sons. Cf. chpt. IV, section III. 

• Omnes, Roland (1999). Understanding Quantum Mechanics. Princeton University Press. ISBN 0-691-00435-8. 
OCLC 39849482. 

• Scerri, Eric R., 2006. The Periodic Table: Its Story and Its Significance. Oxford University Press. Considers the 
extent to which chemistry and the periodic system have been reduced to quantum mechanics. ISBN 
0-19-530573-6 

• Transnational College of Lex (1996). What is Quantum Mechanics? A Physics Adventure. Language Research 
Foundation, Boston. ISBN 0-9643504-1-6. OCLC 34661512. 

• von Neumann, John (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press. 
ISBN 0691028931. 

• Hermann Weyl, 1950. The Theory of Groups and Quantum Mechanics, Dover Publications. 

• D. Greenberger, K. Hentschel, F. Weinert, eds., 2009. Compendium of quantum physics, Concepts, experiments, 
history and philosophy, Springer- Verlag, Berlin, Heidelberg. 

Further reading 

• Bohm, David (1989). Quantum Theory. Dover Publications. ISBN 0-486-65969-0. 

• Eisberg, Robert; Resnick, Robert (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles 
(2nd ed.). Wiley. ISBN 0-471-87373-X. 

• Liboff, Richard L. (2002). Introductory Quantum Mechanics. Addison-Wesley. ISBN 0-8053-8714-5. 

• Merzbacher, Eugen (1998). Quantum Mechanics. Wiley, John & Sons, Inc. ISBN 0-471-88702-1. 

• Sakurai, J. J. (1994). Modern Quantum Mechanics. Addison Wesley. ISBN 0-201-53929-2. 

• Shankar, R. (1994). Principles of Quantum Mechanics. Springer. ISBN 0-306-44790-8. 

External links 

General 

T471 
The Modern Revolution in Physics - an online textbook. 

J. O'Connor and E. F. Robertson: A history of quantum mechanics. 

[49] 
Introduction to Quantum Theory at Quantiki. 

Quantum Physics Made Relatively Simple : three video lectures by Hans Bethe 

H is for h-bar. 

[52] 

Quantum Mechanics Books Collection : Collection of free books 
Course material 

[53] 

Doron Cohen: Lecture notes in Quantum Mechanics (comprehensive, with advanced topics). 

MIT OpenCourseWare: Chemistry [54] . See 5.61 [55] , 5.73 [56] , and 5.74 [57] 

MIT OpenCourseWare: Physics [58] . See 8.04 [59] , 8.05 [60] , and 8.06 [61] 

Stanford Continuing Education PHY 25: Quantum Mechanics by Leonard Susskind, see course description 

[63] Fall 2007 

5Vi Examples in Quantum Mechanics 

Imperial College Quantum Mechanics Course. 

Spark Notes - Quantum Physics. 

Quantum Physics Online : interactive introduction to quantum mechanics (RS applets). 

Experiments to the foundations of quantum physics with single photons. 

Motion Mountain, Volume IV - A modern introduction to quantum theory, with several animations. 



Quantum mechanics 28 

• AQME : Advancing Quantum Mechanics for Engineers — by T.Barzso, D.Vasileska and G.Klimeck online 

learning resource with simulation tools on nanoHUB 

[711 

• Quantum Mechanics by Martin Plenio 

T721 

• Quantum Mechanics by Richard Fitzpatrick 

FAQs 

[731 

• Many-worlds or relative-state interpretation. 

T741 

• Measurement in Quantum mechanics. 

Media 

T751 

• Everything you wanted to know about the quantum world — archive of articles from New Scientist. 

• Quantum Physics Research from Science Daily 

[771 

• "Quantum Trickery: Testing Einstein's Strangest Theory" . The New York Times. December 27, 2005. 

Philosophy 

T781 

• ""Quantum Mechanics" article by Jenann Ismael. in the Stanford Encyclopedia of Philosophy 

T781 

• ""Measurement in Quantum Theory" article by Henry Krips. in the Stanford Encyclopedia of Philosophy 

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Einstein, John Stachel, editor, Princeton University Press, 1989, Vol. 2, pp. 149-166, in German; see also Einstein's early work on the 

quantum hypothesis, ibid. pp. 134-148). 
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[15] Especially since Werner Heisenberg was awarded the Nobel Prize in Physics in 1932 for the creation of quantum mechanics, the role of Max 

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function eigenvalue, such that the probability is the squared modulus of the complex amplitude 
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De.pons.eu (http://de.pons.eu/deutsch-englisch/eigen) 
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pg=PA79). Chapman and Hall. p. 79. ISBN 0-7487-4446-0. ., 
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edition (http://books.google.com/books?id=5tOtmOFBlCsC&pg=PA215). Jones and Bartlett Publishers, Inc. p. 215. ISBN 0-7637-2470-X. 



Quantum mechanics 



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[28 
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[34 

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[43 
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[45 
[46 
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[48 
[49 
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[53 
[54 
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http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 
http 



//www. physik.fu-berlin.de/~kleinert/b5 

//www. Iightandmatter.com/html_books/6mr/ch01/ch01. html 

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Quantum mechanics 30 

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Quantum field theory 



Quantum field theory (QFT) provides a theoretical framework for constructing quantum mechanical models of 
systems classically described by fields or (especially in a condensed matter context) many-body systems. It is widely 
used in particle physics and condensed matter physics. Most theories in modern particle physics, including the 
Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories. 
Quantum field theories are used in many circumstances, especially those where the number of particles 
fluctuates — for example, in the BCS theory of superconductivity. 

In perturbative quantum field theory, the forces between particles are mediated by other particles. The 
electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons 
mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the 
remaining fundamental force, gravity, but many of the proposed theories postulate the existence of a graviton 
particle which mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected 
while carrying the force, because such detection will imply that the force is not being carried. In addition, the notion 
of "force mediating particle" comes from perturbation theory, and thus does not make sense in a context of bound 
states. 

In QFT photons are not thought of as 'little billiard balls', they are considered to be field quanta - necessarily 
chunked ripples in a field that 'look like' particles. Fermions, like the electron, can also be described as ripples in a 
field, where each kind of fermion has its own field. In summary, the classical visualisation of "everything is particles 
and fields", in quantum field theory, resolves into "everything is particles", which then resolves into "everything is 
fields". In the end, particles are regarded as excited states of a field (field quanta). 

History 

Quantum field theory originated in the 1920s from the problem of creating a quantum mechanical theory of the 
electromagnetic field. In 1926, Max Born, Pascual Jordan, and Werner Heisenberg constructed such a theory by 
expressing the field's internal degrees of freedom as an infinite set of harmonic oscillators and by employing the 
usual procedure for quantizing those oscillators (canonical quantization). Max Plank, a physicist at the University of 
Kiels, observed the behavior at the atomic level of radiation and heat on matter. He observed that the energy 
absorbed or emitted was contained in small, discrete (i.e. individual) energy packets called quanta. This theory 
assumed that no electric charges or currents were present, and today would be called a free field theory. The first 
reasonably complete theory of quantum electrodynamics, which included both the electromagnetic field and 
electrically charged matter (specifically, electrons) as quantum mechanical objects, was created by Paul Dirac in 

[21 

1927. This quantum field theory could be used to model important processes such as the emission of a photon by 
an electron dropping into a quantum state of lower energy, a process in which the number of particles changes — 
one atom in the initial state becomes an atom plus a photon in the final state. It is now understood that the ability to 
describe such processes is one of the most important features of quantum field theory. 

It was evident from the beginning that a proper quantum treatment of the electromagnetic field had to somehow 
incorporate Einstein's relativity theory, which had after all grown out of the study of classical electromagnetism. This 
need to put together relativity and quantum mechanics was the second major motivation in the development of 
quantum field theory. Pascual Jordan and Wolfgang Pauli showed in 1928 that quantum fields could be made to 
behave in the way predicted by special relativity during coordinate transformations (specifically, they showed that 
the field commutators were Lorentz invariant), and in 1933 Niels Bohr and Leon Rosenfeld showed that this result 



Quantum field theory 3 1 

could be interpreted as a limitation on the ability to measure fields at space-like separations, exactly as required by 
relativity. A further boost for quantum field theory came with the discovery of the Dirac equation, a single-particle 
equation obeying both relativity and quantum mechanics, when it was shown that several of its undesirable 
properties (such as negative-energy states) could be eliminated by reformulating the Dirac equation as a quantum 
field theory. This work was performed by Wendell Furry, Robert Oppenheimer, Vladimir Fock, and others. 

The third thread in the development of quantum field theory was the need to handle the statistics of many-particle 
systems consistently and with ease. In 1927, Jordan tried to extend the canonical quantization of fields to the 
many-body wavefunctions of identical particles, a procedure that is sometimes called second quantization. In 1928, 
Jordan and Eugene Wigner found that the quantum field describing electrons, or other fermions, had to be expanded 
using anti-commuting creation and annihilation operators due to the Pauli exclusion principle. This thread of 
development was incorporated into many-body theory, and strongly influenced condensed matter physics and 
nuclear physics. 

Despite its early successes, quantum field theory was plagued by several serious theoretical difficulties. Many 
seemingly-innocuous physical quantities, such as the energy shift of electron states due to the presence of the 
electromagnetic field, gave infinity — a nonsensical result — when computed using quantum field theory. This 
"divergence problem" was solved during the 1940s by Bethe, Tomonaga, Schwinger, Feynman, and Dyson, through 
the procedure known as renormalization. This phase of development culminated with the construction of the modern 
theory of quantum electrodynamics (QED). Beginning in the 1950s with the work of Yang and Mills, QED was 
generalized to a class of quantum field theories known as gauge theories. The 1960s and 1970s saw the formulation 
of a gauge theory now known as the Standard Model of particle physics, which describes all known elementary 
particles and the interactions between them. The weak interaction part of the standard model was formulated by 
Sheldon Glashow, with the Higgs mechanism added by Steven Weinberg and Abdus Salam. The theory was shown 
to be renormalizable and hence consistent by Gerardus 't Hooft and Martinus Veltman. 

Also during the 1970s, parallel developments in the study of phase transitions in condensed matter physics led Leo 
Kadanoff, Michael Fisher and Kenneth Wilson (extending work of Ernst Stueckelberg, Andre Peterman, Murray 
Gell-Mann and Francis Low) to a set of ideas and methods known as the renormalization group. By providing a 
better physical understanding of the renormalization procedure invented in the 1940s, the renormalization group 
sparked what has been called the "grand synthesis" of theoretical physics, uniting the quantum field theoretical 
techniques used in particle physics and condensed matter physics into a single theoretical framework. 

The study of quantum field theory is alive and flourishing, as are applications of this method to many physical 
problems. It remains one of the most vital areas of theoretical physics today, providing a common language to many 
branches of physics. 

Principles of quantum field theory 
Classical fields and quantum fields 

Quantum mechanics, in its most general formulation, is a theory of abstract operators (observables) acting on an 
abstract state space (Hilbert space), where the observables represent physically-observable quantities and the state 
space represents the possible states of the system under study. Furthermore, each observable corresponds, in a 
technical sense, to the classical idea of a degree of freedom. For instance, the fundamental observables associated 
with the motion of a single quantum mechanical particle are the position and momentum operators x an d P ■ 
Ordinary quantum mechanics deals with systems such as this, which possess a small set of degrees of freedom. 
(It is important to note, at this point, that this article does not use the word "particle" in the context of wave— particle 
duality. In quantum field theory, "particle" is a generic term for any discrete quantum mechanical entity, such as an 
electron or photon, which can behave like classical particles or classical waves under different experimental 
conditions.) 



Quantum field theory 32 

A quantum field is a quantum mechanical system containing a large, and possibly infinite, number of degrees of 
freedom. This is not as exotic a situation as one might think (e.g., in an infinite-dimensional vector space, a vector is 
just a function as ordinary as f(x) = x A 2; which is, of course, familiar territory). A classical field contains a set of 
degrees of freedom at each point of space; for instance, the classical electromagnetic field defines two vectors — the 
electric field and the magnetic field — that can in principle take on distinct values for each position r . When the 
field as a whole is considered as a quantum mechanical system, its observables form an infinite (in fact uncountable) 
set, because r is continuous. 

Furthermore, the degrees of freedom in a quantum field are arranged in "repeated" sets. For example, the degrees of 
freedom in an electromagnetic field can be grouped according to the position r , with exactly two vectors for each 
r ■ Note that r is an ordinary number that "indexes" the observables; it is not to be confused with the position 
operator x encountered in ordinary quantum mechanics, which is an observable. (Thus, ordinary quantum 
mechanics is sometimes referred to as "zero-dimensional quantum field theory", because it contains only a single set 
of observables.) 

It is also important to note that there is nothing special about r because, as it turns out, there is generally more than 
one way of indexing the degrees of freedom in the field. 

In the following sections, we will show how these ideas can be used to construct a quantum mechanical theory with 
the desired properties. We will begin by discussing single-particle quantum mechanics and the associated theory of 
many-particle quantum mechanics. Then, by finding a way to index the degrees of freedom in the many-particle 
problem, we will construct a quantum field and study its implications. 

Single-particle and many-particle quantum mechanics 

In ordinary quantum mechanics, the time-dependent one-dimensional Schrodinger equation describing the time 
evolution of the quantum state of a single non-relativistic particle is 






\m) = ^ t \m), 



2m. dx 1 
where mis the particle's mass, 1/is the applied potential, and \ip\ denotes the quantum state (we are using 

bra-ket notation). 

We wish to consider how this problem generalizes to TV" particles. There are two motivations for studying the 

many-particle problem. The first is a straightforward need in condensed matter physics, where typically the number 

23 

of particles is on the order of Avogadro's number (6.0221415 x 10 ). The second motivation for the many-particle 
problem arises from particle physics and the desire to incorporate the effects of special relativity. If one attempts to 
include the relativistic rest energy into the above equation (in quantum mechanics where position is an observable), 
the result is either the Klein-Gordon equation or the Dirac equation. However, these equations have many 
unsatisfactory qualities; for instance, they possess energy eigenvalues which extend to — °°, so that there seems to be 
no easy definition of a ground state. It turns out that such inconsistencies arise from relativistic wavefunctions 
having a probabilistic interpretation in position space, as probability conservation is not a relativistically covariant 
concept. In quantum field theory, unlike in quantum mechanics, position is not an observable, and thus, one does not 
need the concept of a position-space probability density. For quantum fields whose interaction can be treated 
perturbatively, this is equivalent to neglecting the possibility of dynamically creating or destroying particles, which 
is a crucial aspect of relativistic quantum theory. Einstein's famous mass-energy relation allows for the possibility 
that sufficiently massive particles can decay into several lighter particles, and sufficiently energetic particles can 
combine to form massive particles. For example, an electron and a positron can annihilate each other to create 
photons. This suggests that a consistent relativistic quantum theory should be able to describe many -particle 
dynamics. 

Furthermore, we will assume that the _/y particles are indistinguishable. As described in the article on identical 
particles, this implies that the state of the entire system must be either symmetric (bosons) or antisymmetric 



Quantum field theory 33 

(fermions) when the coordinates of its constituent particles are exchanged. These multi-particle states are rather 
complicated to write. For example, the general quantum state of a system of _/\T bosons is written as 



|0i • - • 0w) = y 3 m 3 ' J2 l0 P (i))---l0 P (iv)> 3 

p£S N 

where 10^) are the single-particle states, Nj is the number of particles occupying state j , and the sum is taken 

over all possible permutations p acting on JV elements. In general, this is a sum of j\M( iV factorial) distinct 
terms, which quickly becomes unmanageable as _/y increases. The way to simplify this problem is to turn it into a 
quantum field theory. 

Second quantization 

In this section, we will describe a method for constructing a quantum field theory called second quantization. This 
basically involves choosing a way to index the quantum mechanical degrees of freedom in the space of multiple 
identical-particle states. It is based on the Hamiltonian formulation of quantum mechanics; several other approaches 
exist, such as the Feynman path integral, which uses a Lagrangian formulation. For an overview, see the article on 
quantization. 

Second quantization of bosons 

For simplicity, we will first discuss second quantization for bosons, which form perfectly symmetric quantum states. 
Let us denote the mutually orthogonal single-particle states by |0i), 102), |03)i an d so on - For example, the 
3-particle state with one particle in state \(j)i) and two in state |0 2 ) is 

^ [|01>|02}|02> + |02}|0l)|02) + |02)|0 2 )|0l)] • 

The first step in second quantization is to express such quantum states in terms of occupation numbers, by listing 
the number of particles occupying each of the single-particle states 10]), |02), etc - This is simply another way of 
labelling the states. For instance, the above 3-particle state is denoted as 

|1,2,0,0,0,---). 
The next step is to expand the _/y -particle state space to include the state spaces for all possible values of _/y . This 
extended state space, known as a Fock space, is composed of the state space of a system with no particles (the 
so-called vacuum state), plus the state space of a 1 -particle system, plus the state space of a 2-particle system, and so 
forth. It is easy to see that there is a one-to-one correspondence between the occupation number representation and 
valid boson states in the Fock space. 

At this point, the quantum mechanical system has become a quantum field in the sense we described above. The 
field's elementary degrees of freedom are the occupation numbers, and each occupation number is indexed by a 
number j ■ ■ ■, indicating which of the single-particle states |0i), 102} 1 " ' ' 107'} ' ' -it refers to. 
The properties of this quantum field can be explored by defining creation and annihilation operators, which add and 
subtract particles. They are analogous to "ladder operators" in the quantum harmonic oscillator problem, which 
added and subtracted energy quanta. However, these operators literally create and annihilate particles of a given 
quantum state. The bosonic annihilation operator Q^and creation operator a > have the following effects: 

a 2 \N u N 2 , N 3 ,---) = Jn~ 2 \ N u (JV 2 - 1), N 3 , ■ ■ ■}, 



4\N U N 2 , N 3 , ...) = JN 2 + 1\ N u (N 2 + 1), JV 3 , ■ ■ ■}. 
It can be shown that these are operators in the usual quantum mechanical sense, i.e. linear operators acting on the 
Fock space. Furthermore, they are indeed Hermitian conjugates, which justifies the way we have written them. They 
can be shown to obey the commutation relation 



Quantum field theory 34 



[a t ,aj] = , a], a] =0 , a t ,a] = S ij} 



where § stands for the Kronecker delta. These are precisely the relations obeyed by the ladder operators for an 
infinite set of independent quantum harmonic oscillators, one for each single-particle state. Adding or removing 
bosons from each state is therefore analogous to exciting or de-exciting a quantum of energy in a harmonic 
oscillator. 

The Hamiltonian of the quantum field (which, through the Schrodinger equation, determines its dynamics) can be 
written in terms of creation and annihilation operators. For instance, the Hamiltonian of a field of free 
(non-interacting) bosons is 

H = ^E k a\a k , 

k 
where E k is the energy of the fc -th single-particle energy eigenstate. Note that 

a \ a k\ ■■ -,N k ,-- ■) = N k \ ■ ■■ ,N k ,- ■■}. 

Second quantization of fermions 

It turns out that a different definition of creation and annihilation must be used for describing fermions. According to 
the Pauli exclusion principle, fermions cannot share quantum states, so their occupation numbers AT; can only take 
on the value or 1. The fermionic annihilation operators c and creation operators c t are defined by their actions on 
a Fock state thus 

> = o 

) = (-l) {Ni+ - +N ^ ) \N 1 ,N 2 ,---,N 3 = r --) 
} = (-l)^ + - +N ^\N 1 ,N 2 ,...,N J = l,...) 

)=0. 
These obey an anticommutation relation: 

{c l} Cj} = , {cj, cj} = , {c 8 , cj} = Sij. 
One may notice from this that applying a fermionic creation operator twice gives zero, so it is impossible for the 
particles to share single-particle states, in accordance with the exclusion principle. 

Field operators 

We have previously mentioned that there can be more than one way of indexing the degrees of freedom in a quantum 
field. Second quantization indexes the field by enumerating the single-particle quantum states. However, as we have 
discussed, it is more natural to think about a "field", such as the electromagnetic field, as a set of degrees of freedom 
indexed by position. 

To this end, we can define field operators that create or destroy a particle at a particular point in space. In particle 
physics, these operators turn out to be more convenient to work with, because they make it easier to formulate 
theories that satisfy the demands of relativity. 

Single-particle states are usually enumerated in terms of their momenta (as in the particle in a box problem.) We can 
construct field operators by applying the Fourier transform to the creation and annihilation operators for these states. 
For example, the bosonic field annihilation operator d>(r) is 



c,-|JVi 


N 2 ,- 


■,N 3 


= 0, 


CjWi 


N 2 ,- 


■,Nj 


= 1, 


c}\ Nl 


N 2 ,- 


-,iV, 


= 0, 


c}\ Nl 


N 2 ,- 


-,N 3 


= 1, 



0(r)^ f 5>^. 



3 
The bosonic field operators obey the commutation relation 



[0(r),0(rO]=O , [0t(r),0t( r ')]=O , [0(r), 0t( r ')] = S \r - r') 



Quantum field theory 35 

where S(x) stands for the Dirac delta function. As before, the fermionic relations are the same, with the 

commutators replaced by anticommutators. 

It should be emphasized that the field operator is not the same thing as a single-particle wavefunction. The former is 
an operator acting on the Fock space, and the latter is just a scalar field. However, they are closely related, and are 
indeed commonly denoted with the same symbol. If we have a Hamiltonian with a space representation, say 

where the indices \ and j run over all particles, then the field theory Hamiltonian is 

h 2 



H = 

2m 



d\ f (r)VV(r) + f&r fdV (f>\r)<j) i {r')U(\r -r'\)(f>{r')(j)(r). 



This looks remarkably like an expression for the expectation value of the energy, with (j) playing the role of the 
wavefunction. This relationship between the field operators and wavefunctions makes it very easy to formulate field 
theories starting from space-projected Hamiltonians. 

Implications of quantum field theory 

Unification of fields and particles 

The "second quantization" procedure that we have outlined in the previous section takes a set of single-particle 
quantum states as a starting point. Sometimes, it is impossible to define such single-particle states, and one must 
proceed directly to quantum field theory. For example, a quantum theory of the electromagnetic field must be a 
quantum field theory, because it is impossible (for various reasons) to define a wavefunction for a single photon. In 
such situations, the quantum field theory can be constructed by examining the mechanical properties of the classical 
field and guessing the corresponding quantum theory. For free (non-interacting) quantum fields, the quantum field 
theories obtained in this way have the same properties as those obtained using second quantization, such as 
well-defined creation and annihilation operators obeying commutation or anticommutation relations. 

Quantum field theory thus provides a unified framework for describing "field-like" objects (such as the 
electromagnetic field, whose excitations are photons) and "particle-like" objects (such as electrons, which are treated 
as excitations of an underlying electron field), so long as one can treat interactions as "perturbations" of free fields. 
There are still unsolved problems relating to the more general case of interacting fields which may or may not be 
adequately described by perturbation theory. For more on this topic, see Haag's theorem. 

Physical meaning of particle indistinguishability 

The second quantization procedure relies crucially on the particles being identical. We would not have been able to 
construct a quantum field theory from a distinguishable many-particle system, because there would have been no 
way of separating and indexing the degrees of freedom. 

Many physicists prefer to take the converse interpretation, which is that quantum field theory explains what identical 
particles are. In ordinary quantum mechanics, there is not much theoretical motivation for using symmetric 
(bosonic) or antisymmetric (fermionic) states, and the need for such states is simply regarded as an empirical fact. 
From the point of view of quantum field theory, particles are identical if and only if they are excitations of the same 
underlying quantum field. Thus, the question "why are all electrons identical?" arises from mistakenly regarding 
individual electrons as fundamental objects, when in fact it is only the electron field that is fundamental. 



Quantum field theory 36 

Particle conservation and non-conservation 

During second quantization, we started with a Hamiltonian and state space describing a fixed number of particles ( 
j\T), and ended with a Hamiltonian and state space for an arbitrary number of particles. Of course, in many common 
situations _/y is an important and perfectly well-defined quantity, e.g. if we are describing a gas of atoms sealed in a 
box. From the point of view of quantum field theory, such situations are described by quantum states that are 
eigenstates of the number operator jy , which measures the total number of particles present. As with any quantum 
mechanical observable, jCris conserved if it commutes with the Hamiltonian. In that case, the quantum state is 
trapped in the _/V -particle subspace of the total Fock space, and the situation could equally well be described by 
ordinary _/y -particle quantum mechanics. 

For example, we can see that the free-boson Hamiltonian described above conserves particle number. Whenever the 
Hamiltonian operates on a state, each particle destroyed by an annihilation operator fflfc is immediately put back by 
the creation operator a ■ 

On the other hand, it is possible, and indeed common, to encounter quantum states that are not eigenstates of pj , 
which do not have well-defined particle numbers. Such states are difficult or impossible to handle using ordinary 
quantum mechanics, but they can be easily described in quantum field theory as quantum superpositions of states 
having different values of _/\T. For example, suppose we have a bosonic field whose particles can be created or 
destroyed by interactions with a fermionic field. The Hamiltonian of the combined system would be given by the 
Hamiltonians of the free boson and free fermion fields, plus a "potential energy" term such as 

H I = Yu V l( a i + a -q) C k+ q C k, 

k,q 

where a an d a k denotes the bosonic creation and annihilation operators, A and C^ denotes the fermionic 
creation and annihilation operators, and V^is a parameter that describes the strength of the interaction. This 
"interaction term" describes processes in which a fermion in state & either absorbs or emits a boson, thereby being 
kicked into a different eigenstate k + q . (In fact, this type of Hamiltonian is used to describe interaction between 
conduction electrons and phonons in metals. The interaction between electrons and photons is treated in a similar 
way, but is a little more complicated because the role of spin must be taken into account.) One thing to notice here is 
that even if we start out with a fixed number of bosons, we will typically end up with a superposition of states with 

different numbers of bosons at later times. The number of fermions, however, is conserved in this case. 

In condensed matter physics, states with ill-defined particle numbers are particularly important for describing the 

various superfluids. Many of the defining characteristics of a superfluid arise from the notion that its quantum state is 

a superposition of states with different particle numbers. In addition, the concept of a coherent state (used to model 

the laser and the BCS ground state) refers to a state with an ill-defined particle number but a well-defined phase. 

Axiomatic approaches 

The preceding description of quantum field theory follows the spirit in which most physicists approach the subject. 
However, it is not mathematically rigorous. Over the past several decades, there have been many attempts to put 
quantum field theory on a firm mathematical footing by formulating a set of axioms for it. These attempts fall into 
two broad classes. 

The first class of axioms, first proposed during the 1950s, include the Wightman, Osterwalder-Schrader, and 
Haag-Kastler systems. They attempted to formalize the physicists' notion of an "operator-valued field" within the 
context of functional analysis, and enjoyed limited success. It was possible to prove that any quantum field theory 
satisfying these axioms satisfied certain general theorems, such as the spin-statistics theorem and the CPT theorem. 
Unfortunately, it proved extraordinarily difficult to show that any realistic field theory, including the Standard 
Model, satisfied these axioms. Most of the theories that could be treated with these analytic axioms were physically 
trivial, being restricted to low -dimensions and lacking interesting dynamics. The construction of theories satisfying 
one of these sets of axioms falls in the field of constructive quantum field theory. Important work was done in this 



Quantum field theory 37 

area in the 1970s by Segal, Glimm, Jaffe and others. 

During the 1980s, a second set of axioms based on geometric ideas was proposed. This line of investigation, which 
restricts its attention to a particular class of quantum field theories known as topological quantum field theories, is 
associated most closely with Michael Atiyah and Graeme Segal, and was notably expanded upon by Edward Witten, 
Richard Borcherds, and Maxim Kontsevich. However, most physically-relevant quantum field theories, such as the 
Standard Model, are not topological quantum field theories; the quantum field theory of the fractional quantum Hall 
effect is a notable exception. The main impact of axiomatic topological quantum field theory has been on 
mathematics, with important applications in representation theory, algebraic topology, and differential geometry. 

Finding the proper axioms for quantum field theory is still an open and difficult problem in mathematics. One of the 
Millennium Prize Problems — proving the existence of a mass gap in Yang-Mills theory — is linked to this issue. 

Phenomena associated with quantum field theory 

In the previous part of the article, we described the most general properties of quantum field theories. Some of the 
quantum field theories studied in various fields of theoretical physics possess additional special properties, such as 
renormalizability, gauge symmetry, and supersymmetry. These are described in the following sections. 

Renormalization 

Early in the history of quantum field theory, it was found that many seemingly innocuous calculations, such as the 
perturbative shift in the energy of an electron due to the presence of the electromagnetic field, give infinite results. 
The reason is that the perturbation theory for the shift in an energy involves a sum over all other energy levels, and 
there are infinitely many levels at short distances which each give a finite contribution. 

Many of these problems are related to failures in classical electrodynamics that were identified but unsolved in the 
19th century, and they basically stem from the fact that many of the supposedly "intrinsic" properties of an electron 
are tied to the electromagnetic field which it carries around with it. The energy carried by a single electron — its self 
energy — is not simply the bare value, but also includes the energy contained in its electromagnetic field, its attendant 
cloud of photons. The energy in a field of a spherical source diverges in both classical and quantum mechanics, but 
as discovered by Weisskopf, in quantum mechanics the divergence is much milder, going only as the logarithm of 
the radius of the sphere. 

The solution to the problem, presciently suggested by Stueckelberg, independently by Bethe after the crucial 
experiment by Lamb, implemented at one loop by Schwinger, and systematically extended to all loops by Feynman 
and Dyson, with converging work by Tomonaga in isolated postwar Japan, is called renormalization. The technique 
of renormalization recognizes that the problem is essentially purely mathematical, that extremely short distances are 
at fault. In order to define a theory on a continuum, first place a cutoff on the fields, by postulating that quanta 
cannot have energies above some extremely high value. This has the effect of replacing continuous space by a 
structure where very short wavelengths do not exist, as on a lattice. Lattices break rotational symmetry, and one of 
the crucial contributions made by Feynman, Pauli and Villars, and modernized by 't Hooft and Veltman, is a 
symmetry preserving cutoff for perturbation theory. There is no known symmetrical cutoff outside of perturbation 
theory, so for rigorous or numerical work people often use an actual lattice. 

On a lattice, every quantity is finite but depends on the spacing. When taking the limit of zero spacing, we make sure 
that the physically-observable quantities like the observed electron mass stay fixed, which means that the constants 
in the Lagrangian defining the theory depend on the spacing. Hopefully, by allowing the constants to vary with the 
lattice spacing, all the results at long distances become insensitive to the lattice, defining a continuum limit. 

The renormalization procedure only works for a certain class of quantum field theories, called renormalizable 
quantum field theories. A theory is perturbatively renormalizable when the constants in the Lagrangian only 
diverge at worst as logarithms of the lattice spacing for very short spacings. The continuum limit is then well defined 



Quantum field theory 38 

in perturbation theory, and even if it is not fully well defined non-perturbatively, the problems only show up at 
distance scales which are exponentially small in the inverse coupling for weak couplings. The Standard Model of 
particle physics is perturbatively renormalizable, and so are its component theories (quantum 
electrodynamics/electroweak theory and quantum chromodynamics). Of the three components, quantum 
electrodynamics is believed to not have a continuum limit, while the asymptotically free SU(2) and SU(3) weak 
hypercharge and strong color interactions are nonperturbatively well defined. 

The renormalization group describes how renormalizable theories emerge as the long distance low-energy effective 
field theory for any given high-energy theory. Because of this, renormalizable theories are insensitive to the precise 
nature of the underlying high-energy short-distance phenomena. This is a blessing because it allows physicists to 
formulate low energy theories without knowing the details of high energy phenomenon. It is also a curse, because 
once a renormalizable theory like the standard model is found to work, it gives very few clues to higher energy 
processes. The only way high energy processes can be seen in the standard model is when they allow otherwise 
forbidden events, or if they predict quantitative relations between the coupling constants. 

Gauge freedom 

A gauge theory is a theory that admits a symmetry with a local parameter. For example, in every quantum theory the 
global phase of the wave function is arbitrary and does not represent something physical. Consequently, the theory is 
invariant under a global change of phases (adding a constant to the phase of all wave functions, everywhere); this is a 
global symmetry. In quantum electrodynamics, the theory is also invariant under a local change of phase, that is - 
one may shift the phase of all wave functions so that the shift may be different at every point in space-time. This is a 
local symmetry. However, in order for a well-defined derivative operator to exist, one must introduce a new field, 
the gauge field, which also transforms in order for the local change of variables (the phase in our example) not to 
affect the derivative. In quantum electrodynamics this gauge field is the electromagnetic field. The change of local 
gauge of variables is termed gauge transformation. 

In quantum field theory the excitations of fields represent particles. The particle associated with excitations of the 
gauge field is the gauge boson, which is the photon in the case of quantum electrodynamics. 

The degrees of freedom in quantum field theory are local fluctuations of the fields. The existence of a gauge 
symmetry reduces the number of degrees of freedom, simply because some fluctuations of the fields can be 
transformed to zero by gauge transformations, so they are equivalent to having no fluctuations at all, and they 
therefore have no physical meaning. Such fluctuations are usually called "non-physical degrees of freedom" or gauge 
artifacts; usually some of them have a negative norm, making them inadequate for a consistent theory. Therefore, if 
a classical field theory has a gauge symmetry, then its quantized version (i.e. the corresponding quantum field 
theory) will have this symmetry as well. In other words, a gauge symmetry cannot have a quantum anomaly. If a 
gauge symmetry is anomalous (i.e. not kept in the quantum theory) then the theory is non-consistent: for example, in 
quantum electrodynamics, had there been a gauge anomaly, this would require the appearance of photons with 
longitudinal polarization and polarization in the time direction, the latter having a negative norm, rendering the 
theory inconsistent; another possibility would be for these photons to appear only in intermediate processes but not 
in the final products of any interaction, making the theory non unitary and again inconsistent (see optical theorem). 

In general, the gauge transformations of a theory consist of several different transformations, which may not be 
commutative. These transformations are together described by a mathematical object known as a gauge group. 
Infinitesimal gauge transformations are the gauge group generators. Therefore the number of gauge bosons is the 
group dimension (i.e. number of generators forming a basis). 

All the fundamental interactions in nature are described by gauge theories. These are: 

• Quantum electrodynamics, whose gauge transformation is a local change of phase, so that the gauge group is 
U(l). The gauge boson is the photon. 

• Quantum chromodynamics, whose gauge group is SU(3). The gauge bosons are eight gluons. 



Quantum field theory 



39 



• The electroweak Theory, whose gauge group is f7(l) ® SU(2) (a direct product of U(l) and SU(2)). 

• Gravity, whose classical theory is general relativity, admits the equivalence principle which is a form of gauge 
symmetry, however it is explicitly non-renormalizable. 

Supersymmetry 

Supersymmetry assumes that every fundamental fermion has a superpartner that is a boson and vice versa. It was 
introduced in order to solve the so-called Hierarchy Problem, that is, to explain why particles not protected by any 
symmetry (like the Higgs boson) do not receive radiative corrections to its mass driving it to the larger scales (GUT, 
Planck...)- It was soon realized that supersymmetry has other interesting properties: its gauged version is an 
extension of general relativity (Supergravity), and it is a key ingredient for the consistency of string theory. 

The way supersymmetry protects the hierarchies is the following: since for every particle there is a superpartner with 
the same mass, any loop in a radiative correction is cancelled by the loop corresponding to its superpartner, 
rendering the theory UV finite. 

Since no superpartners have yet been observed, if supersymmetry exists it must be broken (through a so-called soft 
term, which breaks supersymmetry without ruining its helpful features). The simplest models of this breaking require 
that the energy of the superpartners not be too high; in these cases, supersymmetry is expected to be observed by 
experiments at the Large Hadron Collider. 

See also 



List of quantum field theories 
Feynman path integral 

Quantum chromodynamics 
Quantum electrodynamics 
Quantum flavordynamics 
Quantum geometrodynamics 

Quantum hydrodynamics 

Quantum magnetodynamics 

Quantum triviality 

Schwinger-Dyson equation 

Relation between Schrodinger's equation and the path integral formulation of 

quantum mechanics 



Basic concepts of quantum mechanics 

Relationship between string theory and quantum field 

theory 

Abraham-Lorentz force 

Form factor 

Photon polarization 

Theoretical and experimental justification for the 

Schrodinger equation 

Invariance mechanics 

Green— Kubo relations 

Green's function (many-body theory) 

Common integrals in quantum field theory 



Further reading 

General readers: 

• Feynman, R.P. (2001) [1964]. The Character of Physical Law. MIT Press. ISBN 0262560038. 

• Feynman, R.P. (2006) [1985]. QED: The Strange Theory of Light and Matter. Princeton University Press. 
ISBN 0691125759. 

• Gribbin, J. (1998). Q is for Quantum: Particle Physics from A to Z. Weidenfeld & Nicolson. ISBN 0297817523. 

• Schumm, Bruce A. (2004) Deep Down Things. Johns Hopkins Univ. Press. Chpt. 4. 

Introductory texts: 

• Bogoliubov, N; Shirkov, D. (1982). Quantum Fields. Benjamin-Cummings. ISBN 0805309837. 

• Frampton, P.H. (2000). Gauge Field Theories. Frontiers in Physics (2nd ed.). Wiley. 

• Greiner, W; Muller, B. (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4. 



Quantum field theory 40 

• Itzykson, C; Zuber, J.-B. (1980). Quantum Field Theory. McGraw-Hill. ISBN 0-07-032071-3. 

• Kane, G.L. (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-1 1749-5. 

• Kleinert, H.; Schulte-Frohlinde, Verena (2001). Critical Properties ofq> -Theories . World Scientific. 
ISBN 981-02-4658-7. 

• Kleinert, H. (2008). Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation . World 
Scientific. ISBN 978-981-279-170-2. 

• Loudon, R (1983). The Quantum Theory of Light. Oxford University Press. ISBN 0-19-851 155-8. 

• Mandl, F.; Shaw, G. (1993). Quantum Field Theory. John Wiley & Sons. ISBN 0-0471-94186-7. 

• Peskin, M.; Schroeder, D. (1995). An Introduction to Quantum Field Theory. Westview Press. 
ISBN 0-201-50397-2. 

• Ryder, L.H. (1985). Quantum Field Theory. Cambridge University Press. ISBN 0-521-33859-X. 

• Srednicki, Mark (2007) Quantum Field Theory. Cambridge Univ. Press. 

• Yndurain, F.J. (1996). Relativistic Quantum Mechanics and Introduction to Field Theory (1st ed.). Springer. 
ISBN 978-3540604532. 

• Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN ISBN 0-691-01019-6. 

Advanced texts: 

• Bogoliubov, N; Logunov, A. A.; Oksak, A.I.; Todorov, I.T. (1990). General Principles of Quantum Field Theory. 
Kluwer Academic Publishers. ISBN 978-0792305408. 

• Weinberg, S. (1995). The Quantum Theory of Fields. 1—3. Cambridge University Press. 

Articles: 

• Gerard 't Hooft (2007) "The Conceptual Basis of Quantum Field Theory in Butterfield, J., and John Earman, 



Frank Wilczek (1999) "Quantum field theory, [8] " Reviews of Modern Physics 71: S83-S95. Also 



eds., Philosophy of Physics, Part A. Elsevier: 661-730 

• Frank Wilczek (1999) "Quantum 
doi=10.1103/Rev. Mod. Phys. 71 . 

External links 

• Stanford Encyclopedia of Philosophy: "Quantum Field Theory, by Meinard Kuhlmann. 

• Siegel, Warren, 2005. Fields. A free text, also available from arXiv:hep-th/9912205. 

• Pedagogic Aids to Quantum Field Theory . Click on "Introduction" for a simplified introduction suitable for 
someone familiar with quantum mechanics. 

• Free condensed matter books and notes . 

ri3i 

• Quantum field theory texts , a list with links to amazon.com. 

• Quantum Field Theory by P. J. Mulders 

• Quantum Field Theory by David Tong 

• Quantum Field Theory Video Lectures by David Tong 

ri7i 

• Quantum Field Theory Lecture Notes by Michael Luke 

n si 

• Quantum Field Theory Video Lectures by Sidney R. Coleman 



Quantum field theory 41 

References 

[I] Weinberg, S. Quantum Field Theory, Vols. I to III, 2000, Cambridge University Press: Cambridge, UK. 

[2] Dirac, P. A.M. (1927). The Quantum Theory of the Emission and Absorption of Radiation, Proceedings of the Royal Society of London, Series 

A, Vol. 114, p. 243. 
[3] Abraham Pais, Inward Bound: Of Matter and F orces in the Physical World ISBN 0-19-851997-4. Pais recounts how his astonishment at the 

rapidity with which Feynman could calculate using his method. Feynman's method is now part of the standard methods for physicists. 
[4] http://users.physik.fu-berlin.de/~kleinert/re.html#B6 

[5] http://users.physik.fu-berlin.de/~kleinert/public_html/kleiner_rebll/psfiles/mvf.pdf 
[6] http://www. Cambridge. org/us/catalogue/catalogue.asp?isbn=0521 864496 
[7] http://www.phys.uu.nl/~thooft/lectures/basisqft.pdf 
[8] http://arxiv.org/abs/hep-th/9803075 
[9] http://plato.stanford.edu/entries/quantum-field-theory/ 
[10] http://insti.physics.sunysb.edu/%7Esiegel/errata.html 

[II] http://quantumfieldtheory.info 

[12] http://www.freebookcentre.net/Physics/Condensed-Matter-Books.html 

[13] http://motls.blogspot.com/2006/01/qft-didactics.html 

[14] http://www.nat.vu.nl/~mulders/QFT-0.pdf 

[15] http://damtp.cam.ac.uk/user/tong/qft/qft.pdf 

[16] http://pirsa.org/index. php?p=speaker&name=David_Tong 

[17] http://www2.physics.utoronto.ca/~luke/PHY2403/References_files/lecturenotes.pdf 

[18] http://www.physics.harvard.edu/about/Phys253.html 



Algebraic quantum field theory 



The Haag-Kastler axiomatic framework for quantum field theory, named after Rudolf Haag and Daniel Kastler, is 
an application to local quantum physics of C*-algebra theory. It is therefore also known as Algebraic Quantum 
Field Theory (AQFT). The axioms are stated in terms of an algebra given for every open set in Minkowski space, 
and mappings between those. 

Let Mink be the category of open subsets of Minkowski space M with inclusion maps as morphisms. We are given a 
covariant functor j\ from Mink to uC*alg, the category of unital C* algebras, such that every morphism in Mink 
maps to a monomorphism in uC*alg {isotony). 

The Poincare group acts continuously on Mink. There exists a pullback of this action, which is continuous in the 
norm topology of J\iM) (Poincare covariance). 

Minkowski space has a causal structure. If an open set V lies in the causal complement of an open set U, then the 
image of the maps 

A{iu,uiiv) 

and 

•A{iv,uuv) 

commute (spacelike commutativity). If TJ is the causal completion of an open set U, then *A(ijjxj)is an 

isomorphism (primitive causality). 

A state with respect to a C*-algebra is a positive linear functional over it with unit norm. If we have a state over 

AiM), we can take the "partial trace" to get states associated with J^.(UMor each open set via the net 

monomorphism. It's easy to show the states over the open sets form a presheaf structure. 

According to the GNS construction, for each state, we can associate a Hilbert space representation of j[(M). Pure 

states correspond to irreducible representations and mixed states correspond to reducible representations. Each 

irreducible (up to equivalence) is called a superselection sector. We assume there is a pure state called the vacuum 

such that the Hilbert space associated with it is a unitary representation of the Poincare group compatible with the 

Poincare covariance of the net such that if we look at the Poincare algebra, the spectrum with respect to 



Algebraic quantum field theory 42 

energy-momentum (corresponding to spacetime translations) lies on and in the positive light cone. This is the 
vacuum sector. 

Suggested reading 

• Haag, Rudolf (1992). Local Quantum Physics: Fields, Particles, Algebras. Springer. 

External links 

• Local Quantum Physics Crossroads - A network of scientists working on Local Quantum Physics 

• Algebraic Quantum Field Theory - AQFT resources at the University of Hamburg 

References 

[1] http://www.lqp.uni-goettingen.de/ 
[2] http://unith.desy.de/research/aqft/ 

Local quantum field theory 

The Haag-Kastler axiomatic framework for quantum field theory, named after Rudolf Haag and Daniel Kastler, is 
an application to local quantum physics of C*-algebra theory. It is therefore also known as Algebraic Quantum 
Field Theory (AQFT). The axioms are stated in terms of an algebra given for every open set in Minkowski space, 
and mappings between those. 

Let Mink be the category of open subsets of Minkowski space M with inclusion maps as morphisms. We are given a 
covariant functor J^ from Mink to uC*alg, the category of unital C* algebras, such that every morphism in Mink 
maps to a monomorphism in uC*alg (isotony). 

The Poincare group acts continuously on Mink. There exists a pullback of this action, which is continuous in the 
norm topology of j\,(M) (Poincare covariance). 

Minkowski space has a causal structure. If an open set V lies in the causal complement of an open set U, then the 
image of the maps 

A{iu,uiiv) 

and 

A(iv,Uuv) 
commute (spacelike commutativity). If jjk the causal completion of an open set U, then Jk.{ijjxj) K an 

isomorphism (primitive causality). 

A state with respect to a C*-algebra is a positive linear functional over it with unit norm. If we have a state over 

AiM), we can take the "partial trace" to get states associated with J[,(U\fov each open set via the net 

monomorphism. It's easy to show the states over the open sets form a presheaf structure. 

According to the GNS construction, for each state, we can associate a Hilbert space representation of j[(M). Pure 

states correspond to irreducible representations and mixed states correspond to reducible representations. Each 

irreducible (up to equivalence) is called a superselection sector. We assume there is a pure state called the vacuum 

such that the Hilbert space associated with it is a unitary representation of the Poincare group compatible with the 

Poincare covariance of the net such that if we look at the Poincare algebra, the spectrum with respect to 

energy-momentum (corresponding to spacetime translations) lies on and in the positive light cone. This is the 

vacuum sector. 



Local quantum field theory 



43 



Suggested reading 

• Haag, Rudolf (1992). Local Quantum Physics: Fields, Particles, Algebras. Springer. 



External links 



in 



Local Quantum Physics Crossroads - A network of scientists working on Local Quantum Physics 
Algebraic Quantum Field Theory - AQFT resources at the University of Hamburg 



Algebraic logic 



In mathematical logic, algebraic logic is the study of logic presented in an algebraic style. 



Algebras as models of logics 

Algebraic logic treats algebraic structures, often bounded lattices, as models (interpretations) of certain logics, 
making logic a branch of order theory. 

In algebraic logic: 

• Variables are tacitly universally quantified over some universe of discourse. There are no existentially quantified 
variables or open formulas; 

• Terms are built up from variables using primitive and defined operations. There are no connectives; 

• Formulas, built from terms in the usual way, can be equated if they are logically equivalent. To express a 
tautology, equate a formula with a truth value; 

• The rules of proof are the substitution of equals for equals, and uniform replacement. Modus ponens remains 
valid, but is seldom employed. 

In the table below, the left column contains one or more logical or mathematical systems, and the algebraic structure 
which are its models are shown on the right in the same row. Some of these structures are either Boolean algebras or 
proper extensions thereof. Modal and other nonclassical logics are typically modeled by what are called "Boolean 
algebras with operators." 

Algebraic formalisms going beyond first-order logic in at least some respects include: 

• Combinatory logic, having the expressive power of set theory; 

• Relation algebra, arguably the paradigmatic algebraic logic, can express Peano arithmetic and most axiomatic set 
theories, including the canonical ZFC. 



logical system 


its models 


Classical sentential logic 


Lindenbaum-Tarski algebra Two-element Boolean algebra 


Intuitionistic propositional logic 


Heyting algebra 


Lukasiewicz logic 


MV-algebra 


Modal logic K 


Modal algebra 


Lewis's S4 


Interior algebra 


Lewis's S5; Monadic predicate logic 


Monadic Boolean algebra 


First-order logic 


Cylindric algebra Polyadic algebra 
Predicate functor logic 


Set theory 


Combinatory logic Relation algebra 



Algebraic logic 44 

History 

On the history of algebraic logic before World War II, see Brady (2000) and Grattan-Guinness (2000) and their 
ample references. On the postwar history, see Maddux (1991) and Quine (1976). 

Algebraic logic has at least two meanings: 

• The study of Boolean algebra, begun by George Boole, and of relation algebra, begun by Augustus DeMorgan, 
extended by Charles Sanders Peirce, and taking definitive form in the work of Ernst Schroder; 

• Abstract algebraic logic, a branch of contemporary mathematical logic. 

Perhaps surprisingly, algebraic logic is the oldest approach to formal logic, arguably beginning with a number of 
memoranda Leibniz wrote in the 1680s, some of which were published in the 19th century and translated into 
English by Clarence Lewis in 1918. But nearly all of Leibniz's known work on algebraic logic was published only in 
1903, after Louis Couturat discovered it in Leibniz's Nachlass. Parkinson (1966) and Loemker (1969) translated 
selections from Couturat's volume into English. 

Brady (2000) discusses the rich historical connections between algebraic logic and model theory. The founders of 
model theory, Ernst Schroder and Leopold Loewenheim, were logicians in the algebraic tradition. Alfred Tarski, the 
founder of set theoretic model theory as a major branch of contemporary mathematical logic, also: 

• Co-discovered Lindenbaum-Tarski algebra; 

• Invented cylindric algebra; 

• Wrote the 1940 paper that revived relation algebra, and that can be seen as the starting point of abstract algebraic 
logic. 

Modern mathematical logic began in 1847, with two pamphlets whose respective authors were Augustus DeMorgan 
and George Boole. They, and later C.S. Peirce, Hugh MacColl, Frege, Peano, Bertrand Russell, and A. N. Whitehead 
all shared Leibniz's dream of combining symbolic logic, mathematics, and philosophy. Relation algebra is arguably 
the culmination of Leibniz's approach to logic. With the exception of some writings by Leopold Loewenheim and 
Thoralf Skolem, algebraic logic went into eclipse soon after the 1910-13 publication of Principia Mathematica, not 
to revive until Tarski's 1940 reexposition of relation algebra. 

Leibniz had no influence on the rise of algebraic logic because his logical writings were little studied before the 
Parkinson and Loemker translations. Our present understanding of Leibniz the logician stems mainly from the work 
of Wolfgang Lenzen, summarized in Lenzen (2004). To see how present-day work in logic and metaphysics can 
draw inspiration from, and shed light on, Leibniz's thought, see Zalta (2000). 

See also 

Abstract algebraic logic 
Algebraic structure 
Boolean algebra (logic) 
Boolean algebra (structure) 
Cylindric algebra 
Lindenbaum-Tarski algebra 
Mathematical logic 
Model theory 
Monadic Boolean algebra 
Predicate functor logic 
Relation algebra 
Universal algebra 



Algebraic logic 45 

References 

• Brady, Geraldine, 2000. From Peirce to Skolem: A neglected chapter in the history of logic. 

T31 
North-Holland/Elsevier Science BV: catalog page , Amsterdam, Netherlands, 625 pages. 

• Burris, Stanley, 2009. The Algebra of Logic Tradition . Stanford Encyclopedia of Philosophy. 

• Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots. Princeton Univ. Press. 

• Lenzen, Wolfgang, 2004, "Leibniz's Logic in Gabbay, D., and Woods, J., eds., Handbook of the History of 
Logic, Vol. 3: The Rise of Modern Logic from Leibniz to Frege. North-Holland: 1-84. 

• Loemker, Leroy (1969 (1956)), Leibniz: Philosophical Papers and Letters, Reidel. 

• Roger Maddux, 1991, "The Origin of Relation Algebras in the Development and Axiomatization of the Calculus 
of Relations," Studia Logica 50: 421-55. 

• Parkinson, G.H.R., 1966. Leibniz: Logical Papers. Oxford Uni. Press. 

• Willard Quine, 1976, "Algebraic Logic and Predicate Functors" in The Ways of Paradox. Harvard Univ. Press: 
283-307. 

• Zalta, E. N., 2000, "A (Leibnizian) Theory of Concepts ," Philosophiegeschichte und logische Analyse / 
Logical Analysis and History of Philosophy 3: 137-183. 

External links 

• Stanford Encyclopedia of Philosophy: "Propositional Consequence Relations and Algebraic Logic — by 
Ramon Jansana. 

References 

[1] http://www.philosophie.uni-osnabrueck.de/Publikationen%20Lenzen/Lenzen%20Leibniz%20Logic.pdf 

[2] http://mally.stanford.edu/Papers/leibniz.pdf 

[3] http://www.elsevier.com/wps/find/bookdescription.cws_home/621535/description 

[4] http://plato.stanford.edu/entries/algebra-logic-tradition/ 

[5] http://mally.stanford.edu/leibniz.pdf 

[6] http://plato.stanford.edu/entries/consequence-algebraic/ 



Quantum logic 46 



Quantum logic 



In quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of 
quantum theory into account. This research area and its name originated in the 1936 paper by Garrett Birkhoff and 
John von Neumann, who were attempting to reconcile the apparent inconsistency of classical boolean logic with the 
facts concerning the measurement of complementary variables in quantum mechanics, such as position and 
momentum. 

Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and 
non-associative many-valued (MV) logic . 

Quantum logic has some properties which clearly distinguish it from classical logic, most notably, the failure of the 
distributive law of propositional logic: 

p and (q or r) = (p and q) or (p and r), 

where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider a 
particle moving on a line and let 

p = "the particle is moving to the right" 

q = "the particle is in the interval [-1,1]" 

r = "the particle is not in the interval [-1,1]" 

then the proposition "q or r" is true, so 

p and (q or r) = p 

On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions on 
simultaneous values of position and momentum than is allowed by the uncertainty principle. So, 

(p and q) or (p and r) = false 

Thus the distributive law fails. 

Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by the 
philosopher Hilary Putnam, at least at one point in his career. This thesis was an important ingredient in Putnam's 
paper Is Logic Empirical? in which he analysed the epistemological status of the rules of propositional logic. Putnam 
attributes the idea that anomalies associated to quantum measurements originate with anomalies in the logic of 
physics itself to the physicist David Finkelstein. However, this idea had been around for some time and had been 
revived several years earlier by George Mackey's work on group representations and symmetry. 

The more common view regarding quantum logic, however, is that it provides a formalism for relating observables, 
system preparation filters and states. In this view, the quantum logic approach resembles more closely the 
C*-algebraic approach to quantum mechanics; in fact with some minor technical assumptions it can be subsumed by 
it. The similarities of the quantum logic formalism to a system of deductive logic may then be regarded more as a 
curiosity than as a fact of fundamental philosophical importance. A more modern approach to the structure of 
quantum logic is to assume that it is a diagram — in the sense of category theory — of classical logics (see David 
Edwards). 

Introduction 

In his classic treatise Mathematical Foundations of Quantum Mechanics, John von Neumann noted that projections 
on a Hilbert space can be viewed as propositions about physical observables. The set of principles for manipulating 
these quantum propositions was called quantum logic by von Neumann and Birkhoff. In his book (also called 
Mathematical Foundations of Quantum Mechanics) G Mackey attempted to provide a set of axioms for this 
propositional system as an orthocomplemented lattice. Mackey viewed elements of this set as potential yes or no 



Quantum logic 47 

questions an observer might ask about the state of a physical system, questions that would be settled by some 
measurement. Moreover Mackey defined a physical observable in terms of these basic questions. Mackey's axiom 
system is somewhat unsatisfactory though, since it assumes that the partially ordered set is actually given as the 
orthocomplemented closed subspace lattice of a separable Hilbert space. Piron, Ludwig and others have attempted to 
give axiomatizations which do not require such explicit relations to the lattice of subspaces. 

The remainder of this article assumes the reader is familiar with the spectral theory of self-adjoint operators on a 
Hilbert space. However, the main ideas can be understood using the finite-dimensional spectral theorem. 

Projections as propositions 

The so-called Hamiltonian formulations of classical mechanics have three ingredients: states, observables and 
dynamics. In the simplest case of a single particle moving in R , the state space is the position-momentum space R . 
We will merely note here that an observable is some real-valued function / on the state space. Examples of 
observables are position, momentum or energy of a particle. For classical systems, the value /(x), that is the value of/ 
for some particular system state x, is obtained by a process of measurement of /. The propositions concerning a 
classical system are generated from basic statements of the form 

• Measurement off yields a value in the interval [a, b] for some real numbers a, b. 

It follows easily from this characterization of propositions in classical systems that the corresponding logic is 
identical to that of some Boolean algebra of subsets of the state space. By logic in this context we mean the rules that 
relate set operations and ordering relations, such as de Morgan's laws. These are analogous to the rules relating 
boolean conjunctives and material implication in classical propositional logic. For technical reasons, we will also 
assume that the algebra of subsets of the state space is that of all Borel sets. The set of propositions is ordered by the 
natural ordering of sets and has a complementation operation. In terms of observables, the complement of the 
proposition {/> a] is {/< a}. 

We summarize these remarks as follows: 

• The proposition system of a classical system is a lattice with a distinguished orthocomplementation operation: 
The lattice operations of meet and join are respectively set intersection and set union. The orthocomplementation 
operation is set complement. Moreover this lattice is sequentially complete, in the sense that any sequence {E.} . of 
elements of the lattice has a least upper bound, specifically the set-theoretic union: 

00 
LVB({E i }) = (JE i . 
i=\ 
In the Hilbert space formulation of quantum mechanics as presented by von Neumann, a physical observable is 

represented by some (possibly unbounded) densely-defined self-adjoint operator A on a Hilbert space H. A has a 
spectral decomposition, which is a projection-valued measure E defined on the Borel subsets of R. In particular, for 
any bounded Borel function/, the following equation holds: 



f(A)= /"/(A)dE(A). 

Jr 



In case / is the indicator function of an interval [a, b], the operator /(A) is a self-adjoint projection, and can be 
interpreted as the quantum analogue of the classical proposition 

• Measurement of A yields a value in the interval [a, b]. 



Quantum logic 48 

The propositional lattice of a quantum mechanical system 

This suggests the following quantum mechanical replacement for the orthocomplemented lattice of propositions in 
classical mechanics. This is essentially Mackey's Axiom VII: 

• The orthocomplemented lattice Q of propositions of a quantum mechanical system is the lattice of closed 
subspaces of a complex Hilbert space H where orthocomplementation of V is the orthogonal complement V . 

Q is also sequentially complete: any pairwise disjoint sequencef V.} . of elements of Q has a least upper bound. Here 

_L ' ' 

disjointness of W and W means W is a subspace of W . The least upper bound of { V } . is the closed internal direct 
sum. 

Henceforth we identify elements of Q with self-adjoint projections on the Hilbert space H. 

The structure of Q immediately points to a difference with the partial order structure of a classical proposition 
system. In the classical case, given a proposition/?, the equations 

I = pV q 

= p A q 
have exactly one solution, namely the set-theoretic complement of p. In these equations / refers to the atomic 
proposition which is identically true and the atomic proposition which is identically false. In the case of the lattice 
of projections there are infinitely many solutions to the above equations. 

Having made these preliminary remarks, we turn everything around and attempt to define observables within the 
projection lattice framework and using this definition establish the correspondence between self-adjoint operators 
and observables: A Mackey observable is a countably additive homomorphism from the orthocomplemented lattice 
of the Borel subsets of R to Q. To say the mapping cp is a countably additive homomorphism means that for any 
sequence {S.} . of pairwise disjoint Borel subsets of R, {cp(5.)}.are pairwise orthogonal projections and 



i i 

oo \ oo 



Theorem. There is a bijective correspondence between Mackey observables and densely-defined self-adjoint 
operators on H. 

This is the content of the spectral theorem as stated in terms of spectral measures. 

Statistical structure 

Imagine a forensics lab which has some apparatus to measure the speed of a bullet fired from a gun. Under carefully 
controlled conditions of temperature, humidity, pressure and so on the same gun is fired repeatedly and speed 
measurements taken. This produces some distribution of speeds. Though we will not get exactly the same value for 
each individual measurement, for each cluster of measurements, we would expect the experiment to lead to the same 
distribution of speeds. In particular, we can expect to assign probability distributions to propositions such as {a < 
speed < b } . This leads naturally to propose that under controlled conditions of preparation, the measurement of a 
classical system can be described by a probability measure on the state space. This same statistical structure is also 
present in quantum mechanics. 

A quantum probability measure is a function P defined on Q with values in [0,1] such that P(0)=0, P(I)=1 and if 
{£■.} . is a sequence of pairwise orthogonal elements of Q then 

(oo \ oo 

i=l / i=l 

The following highly non-trivial theorem is due to Andrew Gleason: 

Theorem. Suppose H is a separable Hilbert space of complex dimension at least 3. Then for any quantum 
probability measure on Q there exists a unique trace class operator S such that 



Quantum logic 49 

P(E) = Ti(SE) 
for any self-adjoint projection E. 

The operator S is necessarily non-negative (that is all eigenvalues are non-negative) and of trace 1 . Such an operator 
is often called a density operator. 

Physicists commonly regard a density operator as being represented by a (possibly infinite) density matrix relative to 
some orthonormal basis. 

For more information on statistics of quantum systems, see quantum statistical mechanics. 

Automorphisms 

An automorphism of Q is a bijective mapping a:Q — > Q which preserves the orthocomplemented structure of Q, that 

is 

(00 \ 00 

J2EA=J2a(E t ) 
i=l / i=\ 

for any sequence {£.}. of pairwise orthogonal self-adjoint projections. Note that this property implies monotonicity 
of a. If P is a quantum probability measure on Q, then E — > a(E) is also a quantum probability measure on Q. By the 
Gleason theorem characterizing quantum probability measures quoted above, any automorphism a induces a 
mapping a* on the density operators by the following formula: 

Ti(a*(S)E) =Tr(Sa(E)). 

The mapping a* is bijective and preserves convex combinations of density operators. This means 

a*(riSx + r 2 S 2 ) — r 1 o;*(5 1 ) + r 2 a*(S 2 ) 
whenever 1 - r + r and r , r are non-negative real numbers. Now we use a theorem of Richard V. Kadison: 

Theorem. Suppose (3 is a bijective map from density operators to density operators which is convexity preserving. 
Then there is an operator U on the Hilbert space which is either linear or conjugate-linear, preserves the inner 
product and is such that 

/?(£) = USU* 

for every density operator S. In the first case we say U is unitary, in the second case U is anti-unitary. 

Remark. This note is included for technical accuracy only, and should not concern most readers. The 
result quoted above is not directly stated in Kadison's paper, but can be reduced to it by noting first that 
p extends to a positive trace preserving map on the trace class operators, then applying duality and 
finally applying a result of Kadison's paper. 

The operator U is not quite unique; if r is a complex scalar of modulus 1, then r U will be unitary or anti-unitary if U 
is and will implement the same automorphism. In fact, this is the only ambiguity possible. 

It follows that automorphisms of Q are in bijective correspondence to unitary or anti-unitary operators modulo 
multiplication by scalars of modulus 1. Moreover, we can regard automorphisms in two equivalent ways: as 
operating on states (represented as density operators) or as operating on Q. 



Quantum logic 50 

Non-relativistic dynamics 

In non-relativistic physical systems, there is no ambiguity in referring to time evolution since there is a global time 
parameter. Moreover an isolated quantum system evolves in a deterministic way: if the system is in a state S at time t 
then at time s > t, the system is in a state F (S). Moreover, we assume 

• The dependence is reversible: The operators F are bijective. 

• The dependence is homogeneous: F = F 

r b s,t s - tfi 

• The dependence is convexity preserving: That is, each F (S) is convexity preserving. 

• The dependence is weakly continuous: The mapping R— > R given by t — > Tr(F (S) E) is continuous for every E 
ing. 

By Kadison's theorem, there is a 1 -parameter family of unitary or anti-unitary operators {U } such that 

F s , t (s) = u a . t su;_ t 

In fact, 

Theorem. Under the above assumptions, there is a strongly continuous 1 -parameter group of unitary operators {U } 
such that the above equation holds. 

Note that it easily from uniqueness from Kadison's theorem that 

U t+a = tr{t,s)U t U a 

where o(t,s) has modulus 1. Now the square of an anti-unitary is a unitary, so that all the U are unitary. The 
remainder of the argument shows that o(t,s) can be chosen to be 1 (by modifying each U by a scalar of modulus 1.) 

Pure states 

A convex combinations of statistical states S and S is a state of the form S = p S +p S where p , p are 
non-negative and p + p =1. Considering the statistical state of system as specified by lab conditions used for its 
preparation, the convex combination S can be regarded as the state formed in the following way: toss a biased coin 
with outcome probabilities P V P 1 and depending on outcome choose system prepared to S or S 

Density operators form a convex set. The convex set of density operators has extreme points; these are the density 
operators given by a projection onto a one-dimensional space. To see that any extreme point is such a projection, 
note that by the spectral theorem S can be represented by a diagonal matrix; since S is non-negative all the entries are 
non-negative and since S has trace 1, the diagonal entries must add up to 1. Now if it happens that the diagonal 
matrix has more than one non-zero entry it is clear that we can express it as a convex combination of other density 
operators. 

The extreme points of the set of density operators are called pure states. If S is the projection on the 1 -dimensional 
space generated by a vector i|> of norm 1 then 

Tt(SE) = <£ty#) 

for any E in Q. In physics jargon, if 

s = |VWI, 

where o|> has norm 1, then 

Tr(SE) = (ij>\E\\l>). 
Thus pure states can be identified with rays in the Hilbert space H. 



Quantum logic 51 

The measurement process 

Consider a quantum mechanical system with lattice Q which is in some statistical state given by a density operator S. 
This essentially means an ensemble of systems specified by a repeatable lab preparation process. The result of a 
cluster of measurements intended to determine the truth value of proposition E, is just as in the classical case, a 
probability distribution of truth values T and F. Say the probabilities are p for T and q = 1 - p for F. By the previous 
section p = Tr(5 E) and q = Tr(5 (7 - £)). 

Perhaps the most fundamental difference between classical and quantum systems is the following: regardless of what 
process is used to determine E immediately after the measurement the system will be in one of two statistical states: 

• If the result of the measurement is T 

1 -ESE. 



Tv(ES) 

If the result of the measurement is F 

1 



(I-E)S(I-E). 



Tr{(7 - E)S) 

(We leave to the reader the handling of the degenerate cases in which the denominators may be 0.) We now form the 
convex combination of these two ensembles using the relative frequencies p and q. We thus obtain the result that the 
measurement process applied to a statistical ensemble in state S yields another ensemble in statistical state: 

M E (S) = ESE +(I- E)S(I - E). 

We see that a pure ensemble becomes a mixed ensemble after measurement. Measurement, as described above, is a 
special case of quantum operations. 

Limitations 

Quantum logic derived from propositional logic provides a satisfactory foundation for a theory of reversible quantum 
processes. Examples of such processes are the covariance transformations relating two frames of reference, such as 
change of time parameter or the transformations of special relativity. Quantum logic also provides a satisfactory 
understanding of density matrices. Quantum logic can be stretched to account for some kinds of measurement 
processes corresponding to answering yes-no questions about the state of a quantum system. However, for more 
general kinds of measurement operations (that is quantum operations), a more complete theory of filtering processes 
is necessary. Such an approach is provided by the consistent histories formalism. On the other hand, quantum logics 
derived from MV-logic extend its range of applicability to irreversible quantum processes and/or 'open' quantum 
systems. 

In any case, these quantum logic formalisms must be generalized in order to deal with super-geometry (which is 
needed to handle Fermi-fields) and non-commutative geometry (which is needed in string theory and quantum 
gravity theory). Both of these theories use a partial algebra with an "integral" or "trace". The elements of the partial 
algebra are not observables; instead the "trace" yields "greens functions" which generate scattering amplitudes. One 
thus obtains a local S-matrix theory (see D. Edwards). 

Since around 1978 the Flato school (see F. Bayen) has been developing an alternative to the quantum logics 
approach called deformation quantization (see Weyl quantization). 

In 2004, Prakash Panangaden described how to capture the kinematics of quantum causal evolution using System 
BV, a deep inference logic originally developed for use in structural proof theory. Alessio Guglielmi, Lutz 
StraBburger, and Richard Blute have also done work in this area. 



Quantum logic 52 

See also 

• Mathematical formulation of quantum mechanics 

• Multi-valued logic 

• Quasi-set theory 

• HPO formalism (An approach to temporal quantum logic) 

• Quantum field theory 

Further reading 

• S. Auyang, How is Quantum Field Theory Possible?, Oxford University Press, 1995. 

• F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization I, II, 
Ann. Phys. (N.Y.), 111 (1978) pp. 61-110, 111-151. 

• G. Birkhoff and J. von Neumann, The Logic of Quantum Mechanics, Annals of Mathematics, Vol. 37, pp. 
823-843, 1936. 

• D. Cohen, An Introduction to Hilbert Space and Quantum Logic, Springer- Verlag, 1989. This is a thorough but 
elementary and well-illustrated introduction, suitable for advanced undergraduates. 

• David Edwards, The Mathematical Foundations of Quantum Mechanics, Synthese, Volume 42, Number 
1/September, 1979, pp. 1-70. 

• D. Edwards, The Mathematical Foundations of Quantum Field Theory: Fermions, Gauge Fields, and 
Super-symmetry, Part I: Lattice Field Theories, International J. of Theor. Phys., Vol. 20, No. 7 (1981). 

• D. Finkelstein, Matter, Space and Logic, Boston Studies in the Philosophy of Science Vol. V, 1969 

• A. Gleason, Measures on the Closed Subspaces of a Hilbert Space, Journal of Mathematics and Mechanics, 1957. 

• R. Kadison, Isometries of Operator Algebras, Annals of Mathematics, Vol. 54, pp. 325—338, 1951 

• G. Ludwig, Foundations of Quantum Mechanics, Springer- Verlag, 1983. 

• G. Mackey, Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, 1963 (paperback reprint by 
Dover 2004). 

• J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955. Reprinted 
in paperback form. 

• R. Omnes, Understanding Quantum Mechanics, Princeton University Press, 1999. An extraordinarily lucid 
discussion of some logical and philosophical issues of quantum mechanics, with careful attention to the history of 
the subject. Also discusses consistent histories. 

• N. Papanikolaou, Reasoning Formally About Quantum Systems: An Overview, ACM SIGACT News, 36(3), pp. 
51-66,2005. 

• C. Piron, Foundations of Quantum Physics, W. A. Benjamin, 1976. 

• H. Putnam, Is Logic Empirical? , Boston Studies in the Philosophy of Science Vol. V, 1969 

• H. Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications, 1950. 



Quantum logic 



53 



External links 

• Stanford Encyclopedia of Philosophy entry on Quantum Logic and Probability Theory 



[8] 



References 

[1] http://arxiv.org/PS_cache/quant-ph/pdf/0101/0101028v2.pdf Maria Luisa Dalla Chiara and Roberto Giuntini. 2008. Quantum Logic, 

102 pages PDF 

[2] Dalla Chiara, M. L. and Giuntini, R.: 1994, Unsharp quantum logics, Foundations of Physics,, 24, 1 161—1 177. 

[3] http://planetphysics.org/encyclopedia/QuantumLMAlgebraicLogic.html I. C. Baianu. 2009. Quantum LMn Algebraic Logic. 

[4] Georgescu, G. and C. Vraciu. 1970, On the characterization of centered Lukasiewicz algebras., J. Algebra, 16: 486-495. 

[5] Georgescu, G. 2006, N-valued Logics and Lukasiewicz-Moisil Algebras, Axiomathes, 16 (1-2): 123- 

[6] http://cs.bath.ac.Uk/ag/p/BVQuantCausEvol.pdf 

[7] http://alessio.guglielmi.name/res/cos/crt.html#CQE 

[8] http://plato.stanford.edu/entries/qt-quantlog/ 



Quantum computer 



A quantum computer is a device for computation that makes direct 
use of quantum mechanical phenomena, such as superposition and 
entanglement, to perform operations on data. Quantum computers are 
different from traditional computers based on transistors. The basic 
principle behind quantum computation is that quantum properties can 
be used to represent data and perform operations on these data. A 
theoretical model is the quantum Turing machine, also known as the 
universal quantum computer. 

Although quantum computing is still in its infancy, experiments have 
been carried out in which quantum computational operations were 
executed on a very small number of qubits (quantum bit). Both 
practical and theoretical research continues, and many national 
government and military funding agencies support quantum computing 
research to develop quantum computers for both civilian and national 




security purposes, such as cryptanalysis 



[21 



The Bloch sphere is a representation of a qubit, 

the fundamental building block of quantum 

computers. 



If large-scale quantum computers can be built, they will be able to solve certain problems much faster than any 
current classical computers (for example Shor's algorithm). Quantum computers however do not allow one to 
compute functions that are not theoretically computable by classical computers, i.e. they do not alter the 
Church— Turing thesis. The gain is only in efficiency. 



Basis 

A classical computer has a memory made up of bits, where each bit represents either a one or a zero. A quantum 
computer maintains a sequence of qubits. A single qubit can represent a one, a zero, or, crucially, any quantum 
superposition of these; moreover, a pair of qubits can be in any quantum superposition of 4 states, and three qubits in 
any superposition of 8. In general a quantum computer with n qubits can be in an arbitrary superposition of up to 
2" different states simultaneously (this compares to a normal computer that can only be in one of these 2 n states at 
any one time). A quantum computer operates by manipulating those qubits with a fixed sequence of quantum logic 
gates. The sequence of gates to be applied is called a quantum algorithm. 



Quantum computer 



54 



An example of an implementation of qubits for a quantum computer could start with the use of particles with two 
spin states: "down" and "up" (typically written M ) and ||) , or IfJ) and |1) ). But in fact any system possessing 
an observable quantity A which is conserved under time evolution and such that A has at least two discrete and 
sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. This is true because 
any such system can be mapped onto an effective spin- 1/2 system. 



Bits vs. qubits 



Consider first a classical computer that operates on a three-bit 
register. The state of the computer at any time is a probability 
distribution over the 2 3 = gdifferent three-bit strings 000, 
001, 010, 011, 100, 101, 110, 111. If it is a 
deterministic computer, then it is in exactly one of these states 
with probability 1 . However, if it is a probabilistic computer, then 
there is a possibility of it being in any one of a number of different 
states. We can describe this probabilistic state by eight 
nonnegative numbers a,b,c,d,ef,g,h (where a = probability 
computer is in state 0, b = probability computer is in state 01, 
etc.). There is a restriction that these probabilities sum to 1. 






4 



o i°> 



^ |0101) ^ |B) 



<=> l*H5» 



qubits can be in a superposition of all the 
classically allowed states 

Qubits are made up of controlled particles and the 

means of control (e.g. devices that trap particles and 

[3] 
switch them from one state to another). 



The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector (a,b,c,d,ef,g,h), 
called a ket. However, instead of adding to one, the sum of the squares of the coefficient magnitudes, 

lal 2 + |p| 2 + ... + |/l| 2 > must equal one. Moreover, the coefficients are complex numbers. Since states are 
represented by complex wavefunctions, two states being added together will undergo interference. This is a key 
difference between quantum computing and probabilistic classical computing. 

If you measure the three qubits, then you will observe a three-bit string. The probability of measuring a string will 
equal the squared magnitude of that string's coefficients (using our example, probability that we read state as 000 = 

|a| 2 , probability that we read state as 001 = Ifjl 2 , etc.). Thus a measurement of the quantum state with 

coefficients (a,b,...,h) gives the classical probability distribution (lal 2 |6| 2 ... l/il 2 )- We say that the quantum 

state "collapses" to a classical state. 

Note that an eight-dimensional vector can be specified in many different ways, depending on what basis you choose 

for the space. The basis of three-bit strings 000, 001, ..., Ill is known as the computational basis, and is often 

convenient, but other bases of unit-length, orthogonal vectors can also be used. Ket notation is often used to make 

explicit the choice of basis. For example, the state (a,b,c,d,ej,g,h) in the computational basis can be written as 

a |000) + b |001) + c |010) + d |011) + e 1 100} + / |101) + g |110) + h |111) , where, e.g., 

|010)= (0,0,1,0,0,0,0,0). 
The computational basis for a single qubit (two dimensions) is IfJ) = (1,0), |1) = (0,1), but another common basis 
are the eigenvectors of the Pauli-x operator: |+) = —^ (1, ljand |— ) = —7= (1, —1). 

Note that although recording a classical state of n bits, a 2 -dimensional probability distribution, requires an 
exponential number of real numbers, practically we can always think of the system as being exactly one of the n-bit 
strings — we just don't know which one. Quantum mechanically, this is not the case, and all 2" complex coefficients 



Quantum computer 55 

need to be kept track of to see how the quantum system evolves. For example, a 300-qubit quantum computer has a 

300 90 

state described by 2 (approximately 10 ) complex numbers, more than the number of atoms in the observable 
universe. 

Operation 

While a classical three-bit state and a quantum three-qubit state are both eight-dimensional vectors, they are 
manipulated quite differently for classical or quantum computation. For computing in either case, the system must be 
initialized, for example into the all-zeros string, 1 000) , corresponding to the vector (1,0,0,0,0,0,0,0). In classical 
randomized computation, the system evolves according to the application of stochastic matrices, which preserve that 
the probabilities add up to one (i.e., preserve the LI norm). In quantum computation, on the other hand, allowed 
operations are unitary matrices, which are effectively rotations (they preserve that the sum of the squares add up to 
one, the Euclidean or L2 norm). (Exactly what unitaries can be applied depend on the physics of the quantum 
device.) Consequently, since rotations can be undone by rotating backward, quantum computations are reversible. 
(Technically, quantum operations can be probabilistic combinations of unitaries, so quantum computation really does 
generalize classical computation. See quantum circuit for a more precise formulation.) 

Finally, upon termination of the algorithm, the result needs to be read off. In the case of a classical computer, we 
sample from the probability distribution on the three-bit register to obtain one definite three-bit string, say 000. 
Quantum mechanically, we measure the three-qubit state, which is equivalent to collapsing the quantum state down 
to a classical distribution (with the coefficients in the classical state being the squared magnitudes of the coefficients 
for the quantum state, as described above) followed by sampling from that distribution. Note that this destroys the 
original quantum state. Many algorithms will only give the correct answer with a certain probability, however by 
repeatedly initializing, running and measuring the quantum computer, the probability of getting the correct answer 
can be increased. 

For more details on the sequences of operations used for various quantum algorithms, see universal quantum 
computer, Shor's algorithm, Graver's algorithm, Deutsch-Jozsa algorithm, amplitude amplification, quantum Fourier 
transform, quantum gate, quantum adiabatic algorithm and quantum error correction. 

Potential 

Integer factorization is believed to be computationally infeasible with an ordinary computer for large integers that 
are the product of only a few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantum 
computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a 
quantum computer to decrypt many of the cryptographic systems in use today, in the sense that there would be a 
polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the 
popular public key ciphers are based on the difficulty of factoring integers (or the related discrete logarithm problem 
which can also be solved by Shor's algorithm), including forms of RSA. These are used to protect secure Web pages, 
encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic 
privacy and security. 

However, other existing cryptographic algorithms don't appear to be broken by these algorithms. Some 

public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to 
which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice 

based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time 
algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, 
is a well-studied open problem. It has been proven that applying Graver's algorithm to break a symmetric (secret 
key) algorithm by brute force requires roughly 2 invocations of the underlying cryptographic algorithm, compared 
with roughly 2 n in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would 
have the same security against an attack using Graver's algorithm that AES-128 has against classical brute-force 



Quantum computer 56 

search (see Key size). Quantum cryptography could potentially fulfill some of the functions of public key 
cryptography. 

Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the 
best known classical algorithm have been found for several problems, including the simulation of quantum 
physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving 
Pell's equation. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be 
discovered, although this is considered unlikely. For some problems, quantum computers offer a polynomial 
speedup. The most well-known example of this is quantum database search, which can be solved by Grover's 
algorithm using quadratically fewer queries to the database than are required by classical algorithms. In this case the 
advantage is provable. Several other examples of provable quantum speedups for query problems have subsequently 
been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees. 

Consider a problem that has these four properties: 

1 . The only way to solve it is to guess answers repeatedly and check them, 

2. There are n possible answers to check, 

3. Every possible answer takes the same amount of time to check, and 

4. There are no clues about which answers might be better: generating possibilities randomly is just as good as 
checking them in some special order. 

An example of this is a password cracker that attempts to guess the password for an encrypted file (assuming that the 
password has a maximum possible length). 

For problems with all four properties, the time for a quantum computer to solve this will be proportional to the 
square root of n. That can be a very large speedup, reducing some problems from years to seconds. It can be used to 
attack symmetric ciphers such as Triple DES and AES by attempting to guess the secret key. 

Grover's algorithm can also be used to obtain a quadratic speed-up [over a brute-force search] for a class of problems 
known as NP-complete. 

Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to 
simulate in an efficient manner classically, many believe quantum simulation will be one of the most important 
applications of quantum computing. 

There are a number of practical difficulties in building a quantum computer, and thus far quantum computers have 
only solved trivial problems. David DiVincenzo, of IBM, listed the following requirements for a practical quantum 

t [13] 

computer: 

• scalable physically to increase the number of qubits; 

• qubits can be initialized to arbitrary values; 

• quantum gates faster than decoherence time; 

• universal gate set; 

• qubits can be read easily. 

Quantum decoherence 

One of the greatest challenges is controlling or removing quantum decoherence. This usually means isolating the 
system from its environment as the slightest interaction with the external world would cause the system to decohere. 
This effect is irreversible, as it is non-unitary, and is usually something that should be avoided, if not highly 
controlled. Decoherence times for candidate systems, in particular the transverse relaxation time T (for NMR and 
MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low 
temperature. 

These issues are more difficult for optical approaches as the timescales are orders of magnitude lower and an often 
cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of 



Quantum computer 57 

operating time to decoherence time, hence any operation must be completed much more quickly than the 
decoherence time. 

If the error rate is small enough, it is thought to be possible to use quantum error correction, which corrects errors 
due to decoherence, thereby allowing the total calculation time to be longer than the decoherence time. An often 

_4 

cited figure for required error rate in each gate is 10 . This implies that each gate must be able to perform its task in 
one 10,000th of the decoherence time of the system. 

Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings 
with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's 

2 

algorithm is still polynomial, and thought to be between L and L , where L is the number of bits in the number to be 
factored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, 

4 ri4i 

this implies a need for about 10 qubits without error correction. With error correction, the figure would rise to 

■7 

about 10 qubits. Note that computation time is about £ 2 or about ]^Q 7 steps and on 1 MHz, about 10 seconds. 

A very different approach to the stability-decoherence problem is to create a topological quantum computer with 
anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates. 

Developments 

There are a number of quantum computing candidates, among those: 

ri7i 

Superconductor-based quantum computers (including SQUID-based quantum computers) 
Trapped ion quantum computer 

Optical lattices 

n si 
Topological quantum computer 

Quantum dot on surface (e.g. the Loss-DiVincenzo quantum computer) 

Nuclear magnetic resonance on molecules in solution (liquid NMR) 

Solid state NMR Kane quantum computers 

Electrons on helium quantum computers 

Cavity quantum electrodynamics (CQED) 

Molecular magnet 

Fullerene-based ESR quantum computer 

Optic-based quantum computers (Quantum optics) 

Diamond-based quantum computer 

Bose— Einstein condensate-based quantum computer 

Transistor-based quantum computer - string quantum computers with entrainment of positive holes using an 

electrostatic trap 

Spin-based quantum computer 

T231 

Adiabatic quantum computation 

[241 [25] 

Rare-earth-metal-ion-doped inorganic crystal based quantum computers 

The large number of candidates shows explicitly that the topic, in spite of rapid progress, is still in its infancy. But at 
the same time there is also a vast amount of flexibility. 

In 2005, researchers at the University of Michigan built a semiconductor chip which functioned as an ion trap. Such 
devices, produced by standard lithography techniques, may point the way to scalable quantum computing tools. 
An improved version was made in 2006. 

In 2009, researchers at Yale University created the first rudimentary solid-state quantum processor. The two-qubit 
superconducting chip was able to run elementary algorithms. Each of the two artificial atoms (or qubits) were made 

[97] [2S] 

up of a billion aluminum atoms but they acted like a single one that could occupy two different energy states. 



Quantum computer 



58 



Another team, working at the University of Bristol, also created a silicon-based quantum computing chip, based on 

[291 
quantum optics. The team was able to run Shor's algorithm on the chip. 



Relation to computational complexity theory 

The class of problems that can be efficiently solved by quantum 
computers is called BQP, for "bounded error, quantum, polynomial 
time". Quantum computers only run probabilistic algorithms, so BQP 
on quantum computers is the counterpart of BPP on classical 
computers. It is defined as the set of problems solvable with a 
polynomial-time algorithm, whose probability of error is bounded 
away from one half. A quantum computer is said to "solve" a 
problem if, for every instance, its answer will be right with high 
probability. If that solution runs in polynomial time, then that problem 
is in BQP. 



PSPACE problems 



NP Problems 




BQP 



The suspected relationship of BQP to other 

l 3 °] 
problem spaces. 



BQP is contained in the complexity class #P (or more precisely in the 
associated class of decision problems P ), which is a subclass of 
PSPACE. 

BQP is suspected to be disjoint from NP-complete and a strict superset of P, but that is not known. Both integer 
factorization and discrete log are in BQP. Both of these problems are NP problems suspected to be outside BPP, and 
hence outside P. Both are suspected to not be NP-complete. There is a common misconception that quantum 
computers can solve NP-complete problems in polynomial time. That is not known to be true, and is generally 
suspected to be false 



[31] 



Although quantum computers may be faster than classical computers, those described above can't solve any 
problems that classical computers can't solve, given enough time and memory (however, those amounts might be 
practically infeasible). A Turing machine can simulate these quantum computers, so such a quantum computer could 
never solve an undecidable problem like the halting problem. The existence of "standard" quantum computers does 
not disprove the Church— Turing thesis. It has been speculated that theories of quantum gravity, such as M-theory 
or loop quantum gravity, may allow even faster computers to be built. Currently, it's an open problem to even define 
computation in such theories due to the problem of time, i.e. there's no obvious way to describe what it means for an 
observer to submit input to a computer and later receive output 



132] 



See also 

Timeline of quantum computing 

Quantum bus 

Post-quantum cryptography 

Chemical computer 

Optical computer 

DNA computer 

Molecular computer 

List of emerging technologies 



Quantum computer 59 

References 

[I] " Quantum Computing with Molecules (http://www.media.mit.edu/physics/publications/papers/98.06.sciam/0698gershenfeld.html)" 
article in Scientific American by Neil Gershenfeld and Isaac L. Chuang - a generally accessible overview of quantum computing and so on. 

[2] Quantum Information Science and Technology Roadmap (http://qist.lanl.gov/qcomp_map.shtml) for a sense of where the research is 

heading. 
[3] Waldner, Jean-Baptiste (2007). Nanocomputers and Swarm Intelligence. London: ISTE. p. 157. ISBN 2746215160. 
[4] David P. DiVincenzo (1995). "Quantum Computation". Science 270 (5234): 255-261. doi:10.1126/science.270.5234.255. 
[5] Integer Factoring (http://modular.fas.harvard.edu/edu/Fall2001/124/misc/arjen_lenstra_factoring.pdf) By ARJEN K. LENSTRA - 

Designs, Codes and Cryptography, 19, 101—128 (2000) Kluwer Academic Publishers 
[6] Daniel J. Bernstein, Introduction to Post-Quantum Cryptography (http://pqcrypto.org/www.springer.com/cda/content/document/ 

cda_downloaddocument/9783540887010-cl.pdf). Introduction to Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen (editors). 

Post-quantum cryptography. Springer, Berlin, 2009. ISBN 978-3-540-88701-0 
[7] See also pqcrypto.org (http://pqcrypto.org/), a bibliography maintained by Daniel J. Bernstein and Tanja Lange on cryptography not known 

to be broken by quantum computing. 
[8] Robert J. McEliece. " A public-key cryptosystem based on algebraic coding theory (http://ipnpr.jpl.nasa.gov/progress_report2/42-44/ 

44N.PDF)." Jet Propulsion Laboratory DSN Progress Report 42-44, 1 14-1 16. 
[9] Kobayashi, H.; Gall, F.L. (2006), "Dihedral Hidden Subgroup Problem: A Survey", Information and Media Technologies (J-STAGE) 1 (1): 

178-185 
[10] Bennett C.H., Bernstein E., Brassard G., Vazirani U., The strengths and weaknesses of quantum computation (http://www.es. berkeley. 

edu/~vazirani/pubs/bbbv.ps). SIAM Journal on Computing 26(5): 1510-1523 (1997). 

[II] Quantum Algorithm Zoo (http://www.its.caltech.edu/~sjordan/zoo.html) - Stephen Jordan's Homepage 

[12] The Father of Quantum Computing (http://www.wired.com/science/discoveries/news/2007/02/72734) By Quinn Norton 02.15.2007, 

Wired.com 
[13] David P. DiVincenzo, IBM (2000-04-13). "The Physical Implementation of Quantum Computation" (http://arxiv.org/abs/quant-ph/ 

0002077). . Retrieved 2006-11-17. 
[14] M. I. Dyakonov, Universite Montpellier (2006-10-14). "Is Fault-Tolerant Quantum Computation Really Possible?" (http://arxiv.org/abs/ 

quant-ph/0610117). . Retrieved 2007-02-16. 
[15] Freedman, Michael; Alexei Kitaev, Michael Larsen, Zhenghan Wang (2002-10-20). "Topological Quantum Computation". Bulletin of the 

American Mathematical Society 40 (1): 31-38. doi:10.1090/S0273-0979-02-00964-3. 
[16] Monroe, Don, Anyons: The breakthrough quantum computing needs? (http://www.newscientist.com/channel/fundamentals/ 

mg20026761.700-anyons-the-breakthrough-quantum-computing-needs.html), New Scientist, 1 October 2008 
[17] Clarke, John; Wilhelm, Frank (June 19, 2008). "Superconducting quantum bits" (http://www.nature.com/nature/journal/v453/n7198/ 

fulVnature07128.html). Nature 453 (7198): 1031-1042. doi:10.1038/nature07128. ISSN 0028-0836. PMID 18563154. . 
[18] Nayak, Chetan; Simon, Steven; Stern, Ady (2008). "Nonabelian Anyons and Quantum Computation" (http://arxiv.org/abs/0707.1889). 

Rev Mod Phys 80: 1083.. 
[19] Nizovtsev, A. P.; Kilin, S. Ya.; Jelezko, F.; Gaebal, T.; Popa, I.; Gruber, A.; Wrachtrup, J. (October 19, 2004). "A quantum computer based 

on NV centers in diamond: Optically detected nutations of single electron and nuclear spins" (http://www.springerlink.com/content/ 

5p65541g357 16085/). Optics and Spectroscopy 99 (2): 248-260. doi:10.1134/1.2034610. . 
[20] Wolfgang Gruener, TG Daily (2007-06-01). "Research indicates diamonds could be key to quantum storage" (http://www.tgdaily.com/ 

content/view/32306/118/). . Retrieved 2007-06-04. 
[21] Neumann, P.; Mizuochi, N.; Rempp, F.; Hemmer, P.; Watanabe, H.; Yamasaki, S.; Jacques, V.; Gaebel, T. et al. (June 6, 2008). 

"Multipartite Entanglement Among Single Spins in Diamond" (http://www.sciencemag.org/cgi/content/abstract/320/5881/1326). 

Science 320 (5881): 1326-1329. doi:10.1126/science.H57233. PMID 18535240. . 
[22] Rene Millman, IT PRO (2007-08-03). "Trapped atoms could advance quantum computing" (http://www.itpro.co.uk/news/121086/ 

trapped-atoms-could-advance-quantum-computing.html). . Retrieved 2007-07-26. 
[23] William M Kaminsky, MIT (Date Unknown). "Scalable Superconducting Architecture for Adiabatic Quantum Computation" (http://arxiv. 

org/pdf/quant-ph/0403090). . Retrieved 2007-02-19. 
[24] Ohlsson, N.; Mohan, R. K.; Kroll, S. (January 1, 2002). "Quantum computer hardware based on rare-earth-ion-doped inorganic crystals" 

(http://www.sciencedirect.eom/science/article/B6TVF-44J3RM9-J/2/307aab59dl57ddd2ebb8281f76f89138). Opt. Commun. 201 (1-3): 

71-77. doi:10.1016/S0030-4018(01)01666-2. . 
[25] Longdell, J. J.; Sellars, M. J.; Manson, N. B. (September 23, 2004). "Demonstration of conditional quantum phase shift between ions in a 

solid" (http://prola.aps.org/abstract/PRL/v93/il3/el30503). Phys. Rev. Lett. 93 (13): 130503. doi:10.1103/PhysRevLett.93.130503. 

PMID 15524694. . 
[26] Ann Arbor (2005-12-12). "U-M develops scalable and mass-producible quantum computer chip" (http://www.umich.edu/news/index. 

html?Releases/2005/Dec05/rl21205b). . Retrieved 2006-11-17. 
[27] Dicarlo, L; Chow, JM; Gambetta, JM; Bishop, LS; Johnson, BR; Schuster, DI; Majer, J; Blais, A et al. (2009-06-28). "Demonstration of 

two-qubit algorithms with a superconducting quantum processor" (http://www.nature.com/nature/journal/vaop/ncurrent/pdf/ 

nature08121.pdf). Nature 460 (7252): 240-4. doi:10.1038/nature08121. ISSN 0028-0836. PMID 19561592. . Retrieved 2009-07-02. 



Quantum computer 60 

[28] "Scientists Create First Electronic Quantum Processor" (http://opa.yale. edu/news/article.aspx?id=6764). 2009-07-02. . Retrieved 
2009-07-02. 

[29] New Scientist (2009-09-04). "Code-breaking quantum algorithm runs on a silicon chip" (http://www.newscientist.com/article/ 
dnl7736-codebreaking-quantum-algorithm-run-on-a-silicon-chip.html). . Retrieved 2009-10-14. 

[30] Michael Nielsen and Isaac Chuang (2000). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. 
ISBN 0-521-63503-9. OCLC 174527496. 

[31] Bernstein and Vazirani, Quantum complexity theory, SIAM Journal on Computing, 26(5):1411-1473, 1997. (http://www.cs.berkeley.edu/ 
-vazirani/bv.ps) 

[32] Scott Aaronson, NP-complete Problems and Physical Reality (http://arxiv.org/abs/quant-ph/0502072), ACM SIGACT News, Vol. 36, 
No. 1. (March 2005), pp. 30-52, section 7 "Quantum Gravity": "[...] to anyone who wants a test or benchmark for a favorite quantum gravity 
theory, [author's footnote: That is, one without all the bother of making numerical predictions and comparing them to observation] let me 
humbly propose the following: can you define Quantum Gravity Polynomial-Time? [...] until we can say what it means for a 'user' to specify 
an 'input' and 'later' receive an 'output' — there is no such thing as computation, not even theoretically." (emphasis in original) 

General references 

• Derek Abbott, Charles R. Doering, Carlton M. Caves, Daniel M. Lidar, Howard E. Brandt, Alexander R. 
Hamilton, David K. Ferry, Julio Gea-Banacloche, Sergey M. Bezrukov, and Laszlo B. Kish (2003). "Dreams 
versus Reality: Plenary Debate Session on Quantum Computing". Quantum Information Processing 2 (6): 
449-472. doi:10.1023/B:QINP.0000042203.24782.9a. arXiv:quant-ph/03 10130. (Alternative Location (free) at 
Michigan university's repository Deep Blue (http://hdl.handle.net/2027.42/45526)) 

David P. DiVincenzo (2000). "The Physical Implementation of Quantum Computation". Experimental Proposals 
for Quantum Computation. arXiv:quant-ph/0002077 

David P. DiVincenzo (1995). "Quantum Computation". Science 270 (5234): 255-261. 
doi:10.1126/science.270.5234.255. Table 1 lists switching and dephasing times for various systems. 
Richard Feynman (1982). "Simulating physics with computers". International Journal of Theoretical Physics 21: 
467. doi:10.1007/BF02650179. 

Gregg Jaeger (2006). Quantum Information: An Overview. Berlin: Springer. ISBN 0-387-35725-4. 
OCLC 255569451. 

Michael Nielsen and Isaac Chuang (2000). Quantum Computation and Quantum Information. Cambridge: 
Cambridge University Press. ISBN 0-521-63503-9. OCLC 174527496. 

Stephanie Frank Singer (2005). Linearity, Symmetry, and Prediction in the Hydrogen Atom. New York: Springer. 
ISBN 0-387-24637-1. OCLC 253709076. 

Giuliano Benenti (2004). Principles of Quantum Computation and Information Volume 1. New Jersey: World 
Scientific. ISBN 9-812-38830-3. OCLC 179950736. 

David P. DiVincenzo (2000). "The Physical Implementation of Quantum Computation". Experimental Proposals 
for Quantum Computation. arXiv:quant-ph/0002077. 

Sam Lomonaco Four Lectures on Quantum Computing given at Oxford University in July 2006 (http://www. 
csee. umbc. edu/~lomonaco/Lectures .html#OxfordLectures) 
C. Adami, N.J. Cerf. (1998). "Quantum computation with linear optics". arXiv:quant-ph/9806048vl. 

Joachim Stolze,; Dieter Suter, (2004). Quantum Computing. Wiley-VCH. ISBN 3527404384. 

Ian Mitchell, (1998). "Computing Power into the 21st Century: Moore's Law and Beyond" (http://citeseer.ist. 
psu.edu/mitchell98computing.html). 

Rolf Landauer, (1961). "Irreversibility and heat generation in the computing process" (http://www. research. 
ibm.com/journal/rd/053/ibmrd0503C. pdf). 

Gordon E. Moore (1965). Cramming more components onto integrated circuits. 

R.W. Keyes, (1988). Miniaturization of electronics and its limits. 

M. A. Nielsen,; E. Knill, ; R. Laflamme,. "Complete Quantum Teleportation By Nuclear Magnetic Resonance" 
(http://citeseer.ist.psu.edu/595490.html). 



Quantum computer 61 

• Lieven M.K. Vandersypen,; Constantino S. Yannoni, ; Isaac L. Chuang, (2000). Liquid state NMR Quantum 
Computing. 

• Imai Hiroshi,; Hayashi Masahito, (2006). Quantum Computation and Information. Berlin: Springer. 
ISBN 3540331328. 

• Andre Berthiaume, (1997). "Quantum Computation" (http://citeseer.ist.psu.edu/article/berthiaume97quantum. 
html). 

• Daniel R. Simon, (1994). "On the Power of Quantum Computation" (http://citeseer.ist.psu.edu/simon94power. 
html). Institute of Electrical and Electronic Engineers Computer Society Press. 

• "Seminar Post Quantum Cryptology" (http://www.crypto.rub.de/its_seminar_ss08.html). Chair for 
communication security at the Ruhr-University Bochum. 

• Laura Sanders, (2009). "First programmable quantum computer created" (http://www.sciencenews.org/view/ 
generic/id/49951/title/First_programmable_quantum_computer_created). 

External links 

• Stanford Encyclopedia of Philosophy: " Quantum Computing (http://plato.stanford.edu/entries/qt-quantcomp/ 
)" by Amit Hagar. 

• Quantiki (http://www.quantiki.org/) - Wiki and portal with free-content related to quantum information 
science. 

• jQuantum: Java quantum circuit simulator (http://jquantum.sourceforge.net/jQuantumApplet.html) 

• QCAD: Quantum circuit emulator (http://www.phys.cs.is.nagoya-u.ac.jp/~watanabe/qcad/index.html) 

• C++ Quantum Library (https://gna.org/projects/quantumlibrary) 

• Haskell Library for Quantum computations (http://hackage.haskell.org/cgi-bin/hackage-scripts/package/ 
quantum-arrow) 

• Video Lectures by David Deutsch (http://www.quiprocone.org/Protected/DD_lectures.htm) 

• Lectures at the Institut Henri Poincare (slides and videos) (http://www.quantware.ups-tlse.fr/IHP2006/) 



Quantum chemistry 62 



Quantum chemistry 



Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field 
theory to address problems in chemistry. The description of the electronic behavior of atoms and molecules as 
pertaining to their reactivity is one of the applications of quantum chemistry. Quantum chemistry lies on the border 
between chemistry and physics, and significant contributions have been made by scientists from both fields. It has a 
strong and active overlap with the field of atomic physics and molecular physics, as well as physical chemistry. 

Quantum chemistry mathematically describes the fundamental behavior of matter at the molecular scale. It is, in 
principle, possible to describe all chemical systems using this theory. In practice, only the simplest chemical systems 
may realistically be investigated in purely quantum mechanical terms, and approximations must be made for most 
practical purposes (e.g., Hartree-Fock, post Hartree-Fock or Density functional theory, see computational chemistry 
for more details). Hence a detailed understanding of quantum mechanics is not necessary for most chemistry, as the 
important implications of the theory (principally the orbital approximation) can be understood and applied in simpler 
terms. 

In quantum mechanics the Hamiltonian, or the physical state, of a particle can be expressed as the sum of two 
operators, one corresponding to kinetic energy and the other to potential energy. The Hamiltonian in the Schrodinger 
wave equation used in quantum chemistry does not contain terms for the spin of the electron. 

Solutions of the Schrodinger equation for the hydrogen atom gives the form of the wave function for atomic orbitals, 
and the relative energy of the various orbitals. The orbital approximation can be used to understand the other atoms 
e.g. helium, lithium and carbon. 

History 

The history of quantum chemistry essentially began with the 1838 discovery of cathode rays by Michael Faraday, the 
1859 statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann 
that the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by Max Planck that 
any energy radiating atomic system can theoretically be divided into a number of discrete energy elements e such 
that each of these energy elements is proportional to the frequency v with which they each individually radiate 
energy, as defined by the following formula: 

e = hv 
where h is a numerical value called Planck's Constant. Then, in 1905, to explain the photoelectric effect (1839), i.e., 
that shining light on certain materials can function to eject electrons from the material, Albert Einstein postulated, 
based on Planck's quantum hypothesis, that light itself consists of individual quantum particles, which later came to 
be called photons (1926). In the years to follow, this theoretical basis slowly began to be applied to chemical 
structure, reactivity, and bonding. 

Electronic structure 

The first step in solving a quantum chemical problem is usually solving the Schrodinger equation (or Dirac equation 
in relativistic quantum chemistry) with the electronic molecular Hamiltonian. This is called determining the 
electronic structure of the molecule. It can be said that the electronic structure of a molecule or crystal implies 
essentially its chemical properties. An exact solution for the Schrodinger equation can only be obtained for the 
hydrogen atom. Since all other atomic, or molecular systems, involve the motions of three or more "particles", their 
Schrodinger equations cannot be solved exactly and so approximate solutions must be sought. 



Quantum chemistry 63 

Wave model 

The foundation of quantum mechanics and quantum chemistry is the wave model, in which the atom is a small, 
dense, positively charged nucleus surrounded by electrons. Unlike the earlier Bohr model of the atom, however, the 
wave model describes electrons as "clouds" moving in orbitals, and their positions are represented by probability 
distributions rather than discrete points. The strength of this model lies in its predictive power. Specifically, it 
predicts the pattern of chemically similar elements found in the periodic table. The wave model is so named because 
electrons exhibit properties (such as interference) traditionally associated with waves. See wave-particle duality. 

Valence bond 

Although the mathematical basis of quantum chemistry had been laid by Schrodinger in 1926, it is generally 
accepted that the first true calculation in quantum chemistry was that of the German physicists Walter Heitler and 
Fritz London on the hydrogen (H ) molecule in 1927. Heitler and London's method was extended by the American 
theoretical physicist John C. Slater and the American theoretical chemist Linus Pauling to become the 
Valence-Bond (VB) [or Heitler-London-Slater-Pauling (HLSP)] method. In this method, attention is primarily 
devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical 
chemists' drawings of bonds. 

Molecular orbital 

An alternative approach was developed in 1929 by Friedrich Hund and Robert S. Mulliken, in which electrons are 
described by mathematical functions delocalized over an entire molecule. The Hund-Mulliken approach or 
molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting spectroscopic 
properties better than the VB method. This approach is the conceptional basis of the Hartree-Fock method and 
further post Hartree-Fock methods. 

Density functional theory 

The Thomas-Fermi model was developed independently by Thomas and Fermi in 1927. This was the first attempt 
to describe many-electron systems on the basis of electronic density instead of wave functions, although it was not 
very successful in the treatment of entire molecules. The method did provide the basis for what is now known as 
density functional theory. Though this method is less developed than post Hartree-Fock methods, its significantly 
lower computational requirements (scaling typically no worse than ^3-with respect to n basis functions) allow it to 
tackle larger polyatomic molecules and even macromolecules. This computational affordability and often 
comparable accuracy to MP2 and CCSD (post-Hartree— Fock methods) has made it one of the most popular methods 
in computational chemistry at present. 

Chemical dynamics 

A further step can consist of solving the Schrodinger equation with the total molecular Hamiltonian in order to study 
the motion of molecules. Direct solution of the Schrodinger equation is called quantum molecular dynamics, within 
the semiclassical approximation semiclassical molecular dynamics, and within the classical mechanics framework 
molecular dynamics (MD). Statistical approaches, using for example Monte Carlo methods, are also possible. 

Adiabatic chemical dynamics 

In adiabatic dynamics, interatomic interactions are represented by single scalar potentials called potential energy 
surfaces. This is the Born-Oppenheimer approximation introduced by Born and Oppenheimer in 1927. Pioneering 
applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and 
generalized into the RRKM theory in 1952 by Marcus who took the transition state theory developed by Eyring in 



Quantum chemistry 64 

1935 into account. These methods enable simple estimates of unimolecular reaction rates from a few characteristics 
of the potential surface. 

Non-adiabatic chemical dynamics 

Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surface 
(corresponding to different electronic quantum states of the molecule). The coupling terms are called vibronic 
couplings. The pioneering work in this field was done by Stueckelberg, Landau, and Zener in the 1930s, in their 
work on what is now known as the Landau-Zener transition. Their formula allows the transition probability between 
two diabatic potential curves in the neighborhood of an avoided crossing to be calculated. 

Quantum chemistry and quantum field theory 

The application of quantum field theory (QFT) to chemical systems and theories has become increasingly common 
in the modern physical sciences. One of the first and most fundamentally explicit appearances of this is seen in the 
theory of the photomagneton. In this system, plasmas, which are ubiquitous in both physics and chemistry, are 
studied in order to determine the basic quantization of the underlying bosonic field. However, quantum field theory 
is of interest in many fields of chemistry, including: nuclear chemistry, astrochemistry, sonochemistry, and quantum 
hydrodynamics. Field theoretic methods have also been critical in developing the ab initio Effective Hamiltonian 
theory of semi-empirical pi-electron methods. 

See also 

Atomic physics 

Computational chemistry 

Condensed matter physics 

International Academy of Quantum Molecular Science 

Molecular modelling 

Physical chemistry 

Quantum chemistry computer programs 

Quantum electrochemistry 

QMC@Home 

Theoretical physics 

Further reading 

• Atkins, P.W. Friedman, R. (2005). Molecular Quantum Mechanics , Oxford University Press, 4th edition. ISBN 
978-0199274987 

• Atkins, P.W. Physical Chemistry (Oxford University Press) ISBN 0-19-879285-9 

• Atkins, P.W. Friedman, R. (2008). Quanta, Matter and Change: A Molecular Approach to Physical Change , W. 
H. Freeman. ISBN 978-0716761174 

• Bernard Pullman and Alberte Pullman. 1963. Quantum Biochemistry, New York and London: Academic Press. 

• Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Considers the 
extent to which chemistry and especially the periodic system has been reduced to quantum mechanics. ISBN 
0-19-530573-6. 

• McWeeny, R. Coulson's Valence (Oxford Science Publications) ISBN 0-19-855144-4 

• Karplus M., Porter R.N. (1971). Atoms and Molecules. An introduction for students of physical chemistry , 
Benjamin-Cummings Publishing Company, ISBN 978-0805352184 



Quantum chemistry 65 

• Landau, L.D. and Lifshitz, E.M. Quantum Mechanics:Non-relativistic Theory (Course of Theoretical Physics 
vol.3) (Pergamon Press) 

• Levine, I. (2008). Physical Chemistry , McGraw-Hill Science, 6th edition. ISBN 978-0072538625 (Hardcover) or 
ISBN 978-0071276368 (Paperback) 

• Pauling, L. (1954). General Chemistry. Dover Publications. ISBN 0-486-65622-5. 

• Pauling, L., and Wilson, E. B. (1935/1963). Introduction to Quantum Mechanics with Applications to Chemistry 
(Dover Publications) ISBN 0-486-64871-0 

• Simon, Z. (1976). Quantum Biochemistry and Specific Interactions., Taylor & Francis; ISBN 978-0856260872 
and ISBN 0-85-6260878 . 

External links 

• The Sherrill Group - Notes [2] 

• ChemViz Curriculum Support Resources 

• Early ideas in the history of quantum chemistry 

• The Particle Adventure 

Nobel lectures by quantum chemists 

• Walter Kohn's Nobel lecture 

T71 

• Rudolph Marcus' Nobel lecture 

ro] 

• Robert Mulliken's Nobel lecture 

• Linus Pauling's Nobel lecture 

• John Pople's Nobel lecture 

References 

[1] "Quantum Chemistry" (http://cmm.cit.nih.gov/modeling/guide_documents/quantum_mechanics_document.html). The N1H Guide to 

Molecular Modeling. National Institutes of Health. . Retrieved 2007-09-08. 
[2] http://vergil.chemistry.gatech.edu/notes/index.html 
[3] http://www.shodor.org/chemviz/ 
[4] http://www.quantum-chemistry-history.com/ 
[5] http://particleadventure.org/ 

[6] http://nobelprize.org/chemistry/laureates/1998/kohn-lecture.html 
[7] http://nobelprize.org/chemistry/laureates/1992/marcus-lecture.html 
[8] http://nobelprize.org/chemistry/laureates/1966/mulliken-lecture.html 
[9] http://nobelprize.org/chemistry/laureates/1954/pauling-lecture.html 
[10] http://nobelprize.org/chemistry/laureates/1998/pople-lecture.html 



Density functional theory 66 



Density functional theory 



Electronic structure methods 

Tight binding 

Nearly-free electron model 

Hartree— Fock 

Modern valence bond 

Generalized valence bond 

M0ller— Plesset perturbation theory 

Configuration interaction 

Coupled cluster 

Multi-configurational self-consistent field 

Density functional theory 

Quantum chemistry composite methods 

Quantum Monte Carlo 

kp perturbation theory 

Muffin-tin approximation 

LCAO method 

Density functional theory (DFT) is a quantum mechanical theory used in physics and chemistry to investigate the 
electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the 
condensed phases. With this theory, the properties of a many-electron system can be determined by using 
functionals, i.e. functions of another function, which in this case is the spatially dependent electron density. Hence 
the name density functional theory comes from the use of functionals of the electron density. DFT is among the most 
popular and versatile methods available in condensed-matter physics, computational physics, and computational 
chemistry. 

DFT has been very popular for calculations in solid state physics since the 1970s. In many cases the results of DFT 
calculations for solid-state systems agreed quite satisfactorily with experimental data. Also, the computational costs 
were relatively low when compared to traditional ways which were based on the complicated many-electron 
wavefunction, such as Hartree-Fock theory and its descendants. However, DFT was not considered accurate enough 
for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly 
refined to better model the exchange and correlation interactions. DFT is now a leading method for electronic 
structure calculations in chemistry and solid-state physics. 

Despite the improvements in DFT, there are still difficulties in using density functional theory to properly describe 
intermolecular interactions, especially van der Waals forces (dispersion); charge transfer excitations; transition 
states, global potential energy surfaces and some other strongly correlated systems; and in calculations of the band 
gap in semiconductors. Its poor treatment of dispersion renders DFT unsuitable (at least when used alone) for the 
treatment of systems which are dominated by dispersion (e.g., interacting noble gas atoms) or where dispersion 
competes significantly with other effects (e.g. in biomolecules). The development of new DFT methods designed to 
overcome this problem, by alterations to the functional or by the inclusion of additive terms, is a current research 
topic. 



Density functional theory 67 

Overview of method 

Although density functional theory has its conceptual roots in the Thomas-Fermi model, DFT was put on a firm 
theoretical footing by the two Hohenberg-Kohn theorems (H-K). The original H-K theorems held only for 
non-degenerate ground states in the absence of a magnetic field, although they have since been generalized to 
encompass these. 

The first H-K theorem demonstrates that the ground state properties of a many-electron system are uniquely 
determined by an electron density that depends on only 3 spatial coordinates. It lays the groundwork for reducing the 
many-body problem of N electrons with 3N spatial coordinates to 3 spatial coordinates, through the use of 
functionals of the electron density. This theorem can be extended to the time-dependent domain to develop 
time-dependent density functional theory (TDDFT), which can be used to describe excited states. 

The second H-K theorem defines an energy functional for the system and proves that the correct ground state 
electron density minimizes this energy functional. 

Within the framework of Kohn-Sham DFT, the intractable many-body problem of interacting electrons in a static 
external potential is reduced to a tractable problem of non-interacting electrons moving in an effective potential. The 
effective potential includes the external potential and the effects of the Coulomb interactions between the electrons, 
e.g., the exchange and correlation interactions. Modeling the latter two interactions becomes the difficulty within KS 
DFT. The simplest approximation is the local-density approximation (LDA), which is based upon exact exchange 
energy for a uniform electron gas, which can be obtained from the Thomas-Fermi model, and from fits to the 
correlation energy for a uniform electron gas. Non-interacting systems are relatively easy to solve as the 
wavefunction can be represented as a Slater determinant of orbitals. Further, the kinetic energy functional of such a 
system is known exactly. The exchange-correlation part of the total-energy functional remains unknown and must be 
approximated. 

Another approach, less popular than Kohn-Sham DFT (KS-DFT) but arguably more closely related to the spirit of 
the original H-K theorems, is orbital-free density functional theory (OFDFT), in which approximate functionals are 
also used for the kinetic energy of the non-interacting system. 

Derivation and formalism 

As usual in many-body electronic structure calculations, the nuclei of the treated molecules or clusters are seen as 
fixed (the Born-Oppenheimer approximation), generating a static external potential V in which the electrons are 
moving. A stationary electronic state is then described by a wavefunction ^(r*!, . . . , Fjv) satisfying the 
many-electron Schrodinger equation 



HV 



T + V + U 



vp 



N ^2 N N 

Ira . t-t 



■qj = E^ 



where j^ is the electronic molecular Hamiltonian, _/V"is the number of electrons, jus the J\T -electron kinetic 

energy, f/is the _/\T -electron potential energy from the external field, and fj is the electron-electron interaction 

energy for the _/\T -electron system. The operators j 1 and jj are so-called universal operators as they are the same 

for any system, while f/is system dependent, i.e. non-universal. The difference between having separable 

single-particle problems and the much more complicated many-particle problem arises from the interaction term fj . 
There are many sophisticated methods for solving the many-body Schrodinger equation based on the expansion of 

the wavefunction in Slater determinants. While the simplest one is the Hartree-Fock method, more sophisticated 

approaches are usually categorized as post-Hartree-Fock methods. However, the problem with these methods is the 

huge computational effort, which makes it virtually impossible to apply them efficiently to larger, more complex 

systems. 



Density functional theory 



68 



Here DFT provides an appealing alternative, being much more versatile as it provides a way to systematically map 
the many-body problem, with fj , onto a single-body problem without jj . In DFT the key variable is the particle 
density n(r), which for a normalized \J> is given by 

n{f) =N I d 3 r 2 / d 3 r 3 ■ ■ ■ / d 3 r N ^*(f, r 2 , . . . , r N )V{r, r 2) . . . , f N ) 



This relation can be reversed, i.e. for a given ground-state density no(r)it is possible, in principle, to calculate the 

corresponding ground-state wavefunction ^qOti, . . . , fjv)- in other words, ty^is a un iq ue functional of 71q, 

^o = * [no] 
and consequently the ground-state expectation value of an observable q is also a functional of Uq 

O[n ] = (y[no]\6\y[n ]) 
In particular, the ground-state energy is a functional of Uq 



T + V + U 



*["o] 



V 



v[r [n ] \ can be written explicitly in terms of the 



V 



l[Mcan be written explicitly in terms of the 



E = E[n ] = (V[n ] 
where the contribution of the external potential /^[rigl 
ground-state density TIq 

V[n ] = I V(r)n (r)d 3 r 

More generally, the contribution of the external potential /\p 

density n , 

V[n] = I V(r)n{r)d 3 r 

The functionals T^land ?7[rilare called universal functionals, while ^/[rjlis called a non-universal functional, 
as it depends on the system under study. Having specified a system, i.e., having specified y', one then has to 
minimize the functional 

E[n] = T[n] + U[n] + / V(r)n(r)d 3 r 

with respect to n(r) , assuming one has got reliable expressions for T[n] and U[n] ■ A successful minimization of 

the energy functional will yield the ground-state density fioand thus all other ground-state observables. 

The variational problems of minimizing the energy functional E[n] can be solved by applying the Lagrangian 

method of undetermined multipliers. First, one considers an energy functional that doesn't explicitly have an 
electron-electron interaction energy term, 



E B [n] = (® s [n\ 



T s + V s 



y s [n] 



where J 1 denotes the non-interacting kinetic energy and \/ is an external effective potential in which the particles 
are moving. Obviously, n f^\ = n (^\ if \T is chosen to be 

v s = v + u+(f-t) 

Thus, one can solve the so-called Kohn-Sham equations of this auxiliary non-interacting system, 



L^ +v -^ 



4>i{r) = £i<t>i{r) 
which yields the orbitals (f> t that reproduce the density n{r) of the original many -body system 

N 

n(r) = n s (r) = ^|0,(f)| 2 

i 

The effective single-particle potential can be written in more detail as 



Density functional theory 69 



V s (r) = V(r) + /' t^J. dV + VfccM?)] 



]3 



where the second term denotes the so-called Hartree term describing the electron-electron Coulomb repulsion, while 
the last term Vxci s called the exchange-correlation potential. Here, Vxc mc l U( l es a ll the many-particle 
interactions. Since the Hartree term and Vxc^epend on n{r) , which depends on the (j)^ , which in turn depend on 
V s , the problem of solving the Kohn-Sham equation has to be done in a self-consistent (i.e., iterative) way. Usually 
one starts with an initial guess for n{r) , then calculates the corresponding V^and solves the Kohn-Sham equations 
for the (f> t . From these one calculates a new density and starts again. This procedure is then repeated until 
convergence is reached. 

Approximations (Exchange-correlation functionals) 

The major problem with DFT is that the exact functionals for exchange and correlation are not known except for the 
free electron gas. However, approximations exist which permit the calculation of certain physical quantities quite 
accurately. In physics the most widely used approximation is the local-density approximation (LDA), where the 
functional depends only on the density at the coordinate where the functional is evaluated: 

Exc[n] = / exc(n)n(r)d 3 

The local spin-density approximation (LSDA) is a straightforward generalization of the LDA to include electron 
spin: 

Exc[nh n l\ = J exc^T'^M^d 3 ^ 

Highly accurate formulae for the exchange-correlation energy density £xc( n U n \ )h ave been constructed from 

quantum Monte Carlo simulations of a free electron model. 

Generalized gradient approximations (GGA) are still local but also take into account the gradient of the density at the 

same coordinate: 

Exc[n h n t ] = j e X c(n h n h Wn h Vfi|)n(r)d 3 r. 
Using the latter (GGA) very good results for molecular geometries and ground-state energies have been achieved. 

Potentially more accurate than the GGA functionals are meta-GGA functions. These functionals include a further 
term in the expansion, depending on the density, the gradient of the density and the Laplacian (second derivative) of 
the density. 

Difficulties in expressing the exchange part of the energy can be relieved by including a component of the exact 
exchange energy calculated from Hartree-Fock theory. Functionals of this type are known as hybrid functionals. 

Generalizations to include magnetic fields 

The DFT formalism described above breaks down, to various degrees, in the presence of a vector potential, i.e. a 
magnetic field. In such a situation, the one-to-one mapping between the ground-state electron density and 
wavefunction is lost. Generalizations to include the effects of magnetic fields have led to two different theories: 
current density functional theory (CDFT) and magnetic field functional theory (BDFT). In both these theories, the 
functional used for the exchange and correlation must be generalized to include more than just the electron density. 
In current density functional theory, developed by Vignale and Rasolt, the functionals become dependent on both 
the electron density and the paramagnetic current density. In magnetic field density functional theory, developed by 
Salsbury, Grayce and Harris, the functionals depend on the electron density and the magnetic field, and the 
functional form can depend on the form of the magnetic field. In both of these theories it has been difficult to 
develop functionals beyond their equivalent to LDA, which are also readily implementable computationally. 



Density functional theory 



70 




Applications 

In practice, Kohn-Sham theory can be applied in several distinct ways 

depending on what is being investigated. In solid state calculations, the 

local density approximations are still commonly used along with plane 

wave basis sets, as an electron gas approach is more appropriate for 

electrons delocalised through an infinite solid. In molecular calculations, 

however, more sophisticated functionals are needed, and a huge variety of 

exchange-correlation functionals have been developed for chemical 

applications. Some of these are inconsistent with the uniform electron gas 

approximation, however, they must reduce to LDA in the electron gas limit. 

Among physicists, probably the most widely used functional is the revised 

Perdew-Burke-Ernzerhof exchange model (a direct generalized-gradient 

parametrization of the free electron gas with no free parameters); however, 

this is not sufficiently calorimetrically accurate for gas-phase molecular calculations. In the chemistry community, 

one popular functional is known as BLYP (from the name Becke for the exchange part and Lee, Yang and Parr for 

the correlation part). Even more widely used is B3LYP which is a hybrid functional in which the exchange energy, 

in this case from Becke's exchange functional, is combined with the exact energy from Hartree-Fock theory. Along 

with the component exchange and correlation functionals, three parameters define the hybrid functional, specifying 

how much of the exact exchange is mixed in. The adjustable parameters in hybrid functionals are generally fitted to a 

'training set' of molecules. Unfortunately, although the results obtained with these functionals are usually sufficiently 

accurate for most applications, there is no systematic way of improving them (in contrast to some of the traditional 

wavefunction-based methods like configuration interaction or coupled cluster theory). Hence in the current DFT 

approach it is not possible to estimate the error of the calculations without comparing them to other methods or 

experiments. 



C with isosurface of ground-state electron 
60 

density as calculated with DFT. 



For molecular applications, in particular for hybrid functionals, Kohn-Sham DFT methods are usually implemented 
just like Hartree-Fock itself. 



Thomas— Fermi model 

The predecessor to density functional theory was the Thomas— Fermi model, developed by Thomas and Fermi in 
1927. They used a statistical model to approximate the distribution of electrons in an atom. The mathematical basis 
postulated that electrons are distributed uniformly in phase space with two electrons in every /], 3 of volume. For 
each element of coordinate space volume ^ 3 r we can fill out a sphere of momentum space up to the Fermi 

[7] 

momentum Pf 

(4/3)7rj>J(f) 
Equating the number of electrons in coordinate space to that in phase space gives: 



,-f. 87T r. 

Solving for P/and substituting into the classical kinetic energy formula then leads directly to a kinetic energy 
represented as a functional of the electron density: 



t TF [n] 
T TF [n] 



V 

1ra t 

-C F 



\ n 



l/3\2 



CK 



oc n 



2/3 



im e 



(r) 



n(r)n 2 ' d (r)d d r = C F 



n 



5/3 



(r)d 3 r 



Density functional theory 7 1 

where C F = f — | 

10m e V87r/ 

As such, they were able to calculate the energy of an atom using this kinetic energy functional combined with the 
classical expressions for the nuclear-electron and electron-electron interactions (which can both also be represented 
in terms of the electron density). 

Although this was an important first step, the Thomas— Fermi equation's accuracy is limited because the resulting 
kinetic energy functional is only approximate, and because the method does not attempt to represent the exchange 
energy of an atom as a conclusion of the Pauli principle. An exchange energy functional was added by Dirac in 
1928. 

However, the Thomas— Fermi— Dirac theory remained rather inaccurate for most applications. The largest source of 
error was in the representation of the kinetic energy, followed by the errors in the exchange energy, and due to the 
complete neglect of electron correlation. 

Teller (1962) showed that Thomas— Fermi theory cannot describe molecular bonding. This can be overcome by 
improving the kinetic energy functional. 

The kinetic energy functional can be improved by adding the Weizsacker (1935) correction: 

Tw[n] = 8 m ./ ~wr 

Hohenberg-Kohn Theorem 

l.For N-interacting electrons, E[n] is only functional of the electron density. 

2. E\n GS ] = E GS 

Eqs^s the rea l ground state energy, and TlQsis the real ground state electron density. 

Software supporting DFT 

DFT is supported by many Quantum chemistry and solid state physics codes, often along with other methods. 

See also 

Basis set (chemistry) 

Gas in a box 

Helium atom 

Kohn— Sham equations 

Local density approximation 

Molecule 

Molecular design software 

Molecular modelling 

Quantum chemistry 

List of quantum chemistry and solid state physics software 

List of software for molecular mechanics modeling 

Thomas— Fermi model 

Time-dependent density functional theory 



Density functional theory 72 

Books on DFT 

• R. Dreizler, E. Gross, Density Functional Theory (Plenum Press, New York, 1995). 

• C. Fiolhais, F. Nogueira, M. Marques (eds.), A Primer in Density Functional Theory (Springer- Verlag, 2003). 
[10] 

• Kohanoff, J., Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods 
(Cambridge University Press, 2006). 

• W. Koch, M. C. Holthausen, A Chemist's Guide to Density Functional Theory (Wiley-VCH, Weinheim, ed. 2, 
2002). 

• R. G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 
1989), ISBN 0-19-504279-4, ISBN 0-19-509276-7 (pbk.). 

• N.H. March, Electron Density Theory of Atoms and Molecules (Academic Press, 1992), ISBN 0-12-470525-1. 

• Richard M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2004 

• D. Sholl, J. A. Steckel, Density Functional Theory: A Practical Introduction, Wiley-Interscience, 2009 

Key papers 

L.H. Thomas, The calculation of atomic fields, Proc. Camb. Phil. Soc, 23 542-548 

P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864 [11] 

W. Kohn and L. J. Sham, Phys. Rev. 140 (1965) A1133 [12] 

A. D. Becke, J. Chem. Phys. 98 (1993) 5648 [13] 

C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37 (1988) 785 [14] 

P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98 (1994) 1 1623 [15] 

K. Burke, J. Werschnik, and E. K. U. Gross, Time-dependent density functional theory: Past, present, and future. 

J. Chem. Phys. 123, 062206 [16] (2005). OAI: arXiv.org:cond-mat/0410362 [17] . 

External links 

n 8i 

• Walter Kohn, Nobel Laureate Freeview video interview with Walter on his work developing density 

functional theory by the Vega Science Trust. 

Klaus Capelle, A bird's-eye view of density-functional theory 

Walter Kohn, Nobel Lecture [20] 

T211 
Density functional theory on arxiv.org 

T221 
FreeScience Library -> Density Functional Theory 

TheABCofDFT [23] 

T241 
Density Functional Theory — an introduction 

1251 
Electron Density Functional Theory - Lecture Notes 

References 

[1] Hohenberg, Pierre; Walter Kohn (1964). "Inhomogeneous electron gas". Physical Review 136 (3B): B864— B871. 

doi:10.1103/PhysRev.l36.B864. 
[2] Levy, Mel (1979). "Universal variational functional of electron densities, first-order density matrices, and natural spin-orbitals and solution 

of the v-representability problem". Proceedings of the National Academy of Sciences (United States National Academy of Sciences) 76 (12): 

6062-6065. doi: 10. 1073/pnas.76. 12.6062. 
[3] Vignale, G.; Mark Rasolt (1987). "Density-functional theory in strong magnetic fields". Physical Review Letters (American Physical Society) 

59 (20): 2360-2363. doi:10.1103/PhysRevLett.59.2360. 
[4] Kohn, W.; Sham, L. J. (1965). "Self-consistent equations including exchange and correlation effects". Phys. Rev. 140 (4A): A1133— A1138. 

doi:10.1103/PhysRev.l40.A1133. 
[5] John P. Perdew, Adrienn Ruzsinszky, Jianmin Tao, Viktor N. Staroverov, Gustavo Scuseria and Gabor I. Csonka (2005). "Prescriptions for 

the design and selection of density functional approximations: More constraint satisfaction with fewer fits". J. Chem. Phys. 123: 062201. 

doi:10.1063/l. 1904565. 



Density functional theory 73 

[6] Parr and Yang 1989, p.47 

[7] March 1992, p.24 

[8] Weizsacker, C. F. v. (1935). "Zur Theorie der Kernmassen". Zeitschrift fur Physik 96 (7-8): 431-58. doi:10.1007/BF01337700. 

[9] Parr and Yang 1989, p. 127 

[10] http://www.springerlink.com/content/jyahrga7al29/ 

[11] http://prola.aps.org/abstract/PR/vl36/i3B/pB864_l 

[12] http://prola.aps.org/abstract/PR/vl40/i4A/pAl 133_1 

[13] http://dx.doi.org/10.1063/L464913 

[14] http://prola.aps.org/abstract/PRB/v37/i2/p785_l 

[15] http://dx.doi.org/10.1021/jl00096a001 

[16] http://dx.doi.org/10.1063/L1904586 

[17] http://arxiv.org/abs/cond-mat/0410362 

[18] http ://www. vega.org. uk/video/programme/23 

[19] http://arxiv.org/abs/cond-mat/021 1443 

[20] http://nobelprize.org/chemistry/laureates/1998/kohn-lecture.pdf 

[21] http://xstructure.inr.ac. ru/x-bin/theme3.py?level=l&indexl=447765 

[22] http://freescience. info/books. php?id=30 

[23] http://chem.ps.uci.edu/~kieron/dft/book/gamma/gl.pdf 

[24] http://arxiv.org/abs/physics/9806013 

[25] http://www.fh.huji.ac.il/~roib/LectureNotes/DFT/DFT_Course_Roi_Baer.pdf 



Birefringence 




Birefringence, or double refraction, 

is the decomposition of a ray of light 

into two rays (the ordinary ray and 

the extraordinary ray) when it passes 

through certain types of material, such 

as calcite crystals or boron nitride, 

depending on the polarization of the 

light. This effect can occur only if the 

structure of the material is anisotropic 

(directionally dependent). If the 

material has a single axis of anisotropy 

or optical axis, (i.e. it is uniaxial) birefringence can be formalized by assigning two different refractive indices to the 

material for different polarizations. The birefringence magnitude is then defined by 

An = n e — n 

where n and n are the refractive indices for polarizations parallel (extraordinary) and perpendicular (ordinary) to 

e ° [11 

the axis of anisotropy respectively. 

The reason for birefringence is the fact that in anisotropic media the electric field vector pj and the dielectric 
displacement jj can be nonparallel (namely for the extraordinary polarisation), although being linearly related. 
Birefringence can also arise in magnetic, not dielectric, materials, but substantial variations in magnetic permeability 
of materials are rare at optical frequencies. Liquid crystal materials as used in Liquid Crystal Displays (LCDs) are 

[21 

also birefringent. 



Birefringence 



74 



Creation 

While birefringence is often found naturally (especially in crystals), there are several ways to create it in optically 
isotropic materials. 

• Birefringence results when isotropic materials are deformed such that the isotropy is lost in one direction (i.e., 

131 
stretched or bent). Example 

• Applying an electric field can induce molecules to line up or behave asymmetrically, introducing anisotropy and 
resulting in birefringence, (see Pockels effect) 

• Applying a magnetic field can cause a material to be circularly birefringent, with different indices of refraction 
for oppositely-handed circular polarizations 

• Self alignment of highly polar molecules such as lipids and some surfactants will generate highly birefringent thin 
films (see also Liquid crystal) 



Examples of uniaxial birefringent materials 



Uniaxial materials, at 590 nm 



[4] 



Material 



beryl Be 3 Al 2 (Si0 3 ) 6 



n n An 

o e 

1.602 1.557 -0.045 



calcite CaCO, 



calomel Hg CI 



1.658 1.486 -0.172 
1.973 2.656 +0.683 



ice H 2 Q 



lithium niobate LiNbO, 



1.309 1.313 +0.004 
2.272 2.187 -0.085 



magnesium fluoride MgF 
quartz SiO 



1.380 1.385 +0.006 
1.544 1.553 +0.009 



ruby A1 2 3 
rutile TiO„ 



1.770 1.762 -0.008 
2.616 2.903 +0.287 



peridot (Mg, Fe) 2 Si0 4 
sapphire Al O 



1.690 1.654 -0.036 
1.768 1.760 -0.008 



sodium nitrate NaNO, 



1.587 1.336 -0.251 



tourmaline (complex silicate ) 1.669 1.638 -0.031 



zircon, high ZrSiO, 



zircon, low ZrSiO , 



1.960 2.015 +0.055 
1.920 1.967 +0.047 



Many plastics are birefringent, because their molecules are 'frozen' in a stretched conformation when the plastic is 
moulded or extruded. For example, cellophane is a cheap birefringent material, and Polaroid sheets are commonly 
used to examine for orientation in birefringent plastics like polystyrene and polycarbonate. Birefringent materials are 
used in many devices which manipulate the polarization of light, such as wave plates, polarizing prisms, and Lyot 
filters. 

There are many birefringent crystals: birefringence was first described in calcite crystals by the Danish scientist 
Rasmus Bartholin in 1669. 

Birefringence can be observed in amyloid plaque deposits such as are found in the brains of Alzheimer's patients. 
Modified proteins such as immunoglobulin light chains abnormally accumulate between cells, forming fibrils. 
Multiple folds of these fibers line up and take on a beta-pleated sheet conformation. Congo red dye intercalates 



Birefringence 



75 



between the folds and, when observed under polarized light, causes birefringence. 

Cotton (Gossypium hirsutum) fiber is birefringent because of high levels of cellulosic material in the fiber's 
secondary cell wall. 

Slight imperfections in optical fiber can cause birefringence, which can cause distortion in fiber-optic 
communication; see polarization mode dispersion. The imperfections can be geometrically based, or a result of 
photoelastic effects from loading on the optical fiber. 

Silicon carbide, also known as Moissanite, is strongly birefringent. 



The refractive indices of several (uniaxial) birefringent materials are listed below (at wavelength ~ 590 nm) 



[4] 



Biaxial birefringence 



Biaxial materials, at 590 nm 



[4] 



Material 


n 

a 


\ 


n 

Y 


borax 


1.447 


1.469 


1.472 


epsom salt MgS0 4 -7(H 2 0) 


1.433 


1.455 


1.461 


mica, biotite 


1.595 


1.640 


1.640 


mica, muscovite 


1.563 


1.596 


1.601 


olivine (Mg, Fe) 2 Si0 4 


1.640 


1.660 


1.680 


perovskite CaTiO 


2.300 


2.340 


2.380 


topaz 


1.618 


1.620 


1.627 


ulexite 


1.490 


1.510 


1.520 



Biaxial birefringence, also known as trirefringence, describes an anisotropic material that has more than one axis 

of anisotropy. For such a material, the refractive index tensor n, will in general have three distinct eigenvalues that 

can be labeled n , n„ and n . 
a p y 



Measurement 

Birefringence and related optical effects (such as optical rotation and linear or circular dichroism) can be measured 
by measuring the changes in the polarization of light passing through the material. These measurements are known 
as polarimetry. 

Birefringence of lipid bilayers can be measured using dual polarisation interferometry. This provides a measure of 
the degree of order within these fluid layers and how this order is disrupted when the layer interacts with other 
biomolecules. 

A common feature of optical microscopes is a pair of crossed polarizing filters. Between the crossed polarizers, a 
birefringent sample will appear bright against a dark (isotropic) background. 

For a fixed composition such as calcium carbonate, a crystal such as calcite or its polymorphs, the index of refraction 
depends on the direction of light through the crystal structure. The refraction also depends on composition, and can 
be calculated using the Gladstone-Dale relation. 



Birefringence 



76 



Applications 

Birefringence is widely used in optical devices, such as liquid crystal displays, light modulators, color filters, wave 
plates, optical axis gratings, etc. It also plays an important role in second harmonic generation and many other 
nonlinear processes. It is also utilized in medical diagnostics: needle aspiration of fluid from a gouty joint will reveal 
negatively birefringent urate crystals. In ophthalmology, scanning laser polarimetry utilises the birefringence of the 
retinal nerve fibre layer to indirectly quantify its thickness, which is of use in the assessment and monitoring of 
glaucoma. Birefringence characteristics in sperm heads allow for the selection of spermatozoa for intracytoplasmic 

• • ♦■ [6] 

sperm injection. 

Birefringent filters are also used as spatial low-pass filters in electronic cameras, where the thickness of the crystal is 
controlled to spread the image in one direction, thus increasing the spot-size. This is essential to the proper working 
of all television and electronic film cameras, to avoid spatial aliasing, the folding back of frequencies higher than can 
be sustained by the pixel matrix of the camera. 



Elastic birefringence 

Another form of birefringence is observed in anisotropic elastic materials. In these materials, shear waves split 
according to similar principles as the light waves discussed above. The study of birefringent shear waves in the earth 
is a part of seismology. Birefringence is also used in optical mineralogy to determine the chemical composition, and 
history of minerals and rocks. 

Electromagnetic waves in an anisotropic material 



Effective refractive indices in uniaxial materials 



Propagation 
direction 


Ordinary ray 


Extraordinary ray 


Polarization 


eff 


Polarization 


"eff 


z 


xy-plane 


n 


n/a 


n/a 


ry-plane 


xy-plane 


n 


Z 


n e 


xz-plane 


y 


n 


Jtz-plane 


n e < n < n 


other 


analogous to *z-plane 



The behavior of a light ray that propagates through an anisotropic material is dependent on its polarization. For a 
given propagation direction, there are generally two perpendicular polarizations for which the medium behaves as if 
it had a single effective refractive index. In a uniaxial material, rays with these polarizations are called the 
extraordinary and the ordinary ray (e and o rays), corresponding to the extraordinary and ordinary refractive indices. 
In a biaxial material, there are three refractive indices a, /3, and y, yet only two rays, which are called the fast and the 
slow ray. The slow ray is the ray that has the highest effective refractive index. 

For a uniaxial material with the z axis defined to be the optical axis, the effective refractive indices are as in the table 
on the right. For rays propagating in the xz plane, the effective refractive index of the e polarization varies 
continuously between n and n e , depending on the angle with the z axis. The effective refractive index can be 
constructed from the Index ellipsoid. 



Birefringence 



77 



Mathematical description 

More generally, birefringence can be defined by considering a dielectric permittivity and a refractive index that are 
tensors. Consider a plane wave propagating in an anisotropic medium, with a relative permittivity tensor e, where the 
refractive index n, is defined by n ■ n = e . If the wave has an electric vector of the form: 

E = E expz(k-r-c^t) (2) 
where r is the position vector and t is time, then the wave vector k and the angular frequency w must satisfy 
Maxwell's equations in the medium, leading to the equations: 



-V x V x E 



1. d 2 E w? 

— (e ■ ) ( 3a ) 

c 2 V dt 2 ' 



V - (e ■ E) = (3b) 
where c is the speed of light in a vacuum. Substituting eqn. 2 in eqns. 3a-b leads to the conditions: 

|k| 2 Eo-(k-Eo)k = ^(e-E )W 
k ■ (e ■ E ) = (4b) 

For the matrix product (<e ■ E) often a separate name is used, the dielectric displacement vector TJ). So essentially 

birefringence concerns the general theory of linear relationships between these two vectors in anisotropic media. 

To find the allowed values of k, E can be eliminated from eq 4a. One way to do this is to write eqn 4a in Cartesian 

coordinates, where the x, y and z axes are chosen in the directions of the eigenvectors of e, so that 

^ 2 

e: = u n 2 . 



K 













(4c) 



Hence eqn 4a becomes 



-K -K + 



w 2 nl. 



)E X ~t K x k y £jy -j- k x k z hj z 



(5a) 



k x ky£i/ x -\- { k x k z -\- 



u! 2 n 2 



y -)E y + k y k z E z = (5b) 



k x k z tj x -j- kyk z hjy + \— k x — k + 



Up-Tpi. 



Er = a ( 5c ) 



where E ,E ,E ,k ,k and k are the components of E. and k. This is a set of linear equations in E , E , E , and they 

xyzxyz * l xyz^ 

have a non-trivial solution if their determinant is zero: 



det 



(-*; - k 2 z + 

K x Ky 



K x fCy 

i-kl - hi + 



rl ) 



™y'vz 



k x k z 

If z 

i-kl - kl + 



0(6) 



Multiplying out eqn (6), and rearranging the terms, we obtain 



UJ 



UJ 



2 (kl + kl . kl + kl . kl + kl\ 



+ 



c 4 c 2 y n 2 . n y 



n- 



+ 



hi 



J \ n l n l 



+ 



/..'2 

K _v 

nlnl 



k 



, r , 2l (kl+kl+kl) = 0(7) 



n x n y 



In the case of a uniaxial material, where n = 

X 

(kl kl kl 



n =n and n =n say, eqn 7 can be factorised into 
-j o z e 




kl 

■2 



/• 2 
,2 



,2 



UJ 



= 0.(8) 
n* n^ n^ c L I \n* n^ n^ c* I 

Each of the factors in eqn 8 defines a surface in the space of vectors k — the surface of wave normals. The first 

factor defines a sphere and the second defines an ellipsoid. Therefore, for each direction of the wave normal, two 

wavevectors k are allowed. Values of k on the sphere correspond to the ordinary rays while values on the ellipsoid 

correspond to the extraordinary rays. 



Birefringence 78 

For a biaxial material, eqn (7) cannot be factorized in the same way, and describes a more complicated pair of 
wave-normal surfaces. 

Birefringence is often measured for rays propagating along one of the optical axes (or measured in a 
two-dimensional material). In this case, n has two eigenvalues which can be labeled n and n . n can be diagonalized 
by: 



n = R( X ) 



R-(x) T m 



'nj 0" 
n 2 ^ 

where R(x) is the rotation matrix through an angle X- Rather than specifying the complete tensor n, we may now 
simply specify the magnitude of the birefringence An, and extinction angle x, where An = n - n . 

See also 

• Cotton-Mouton effect 

• Crystal optics 

• John Kerr 

• Periodic poling 

• Dichroism 

External links 

• http://www.olympusmicro.com/primer/lightandcolor/birefringence.html 

• [8] Video of stress birefringence in Polymethylmethacrylate (PMMA or Plexiglas). 

• Application note on the theory of birefringence (see no. 14) 

References 

[1] Eric Weisstein's World of Science on Birefringence (http://scienceworld.wolfram.com/physics/Birefringence.html) 

[2] The Science of Color, by Steven K. Shevell, Optical Society of America. Published 2003. ISBN 04445 125 19 

[3] http://www.oberlin.edu/physics/catalog/demonstrations/optics/birefringence.html 

[4] Elert, Glenn. "Refraction" (http://hypertextbook.com/physics/waves/refraction/). The Physics Hypertextbook. . 

[5] The Use of Birefringence for Predicting the Stiffness of Injection Moulded Polycarbonate Discs (http://www.dep.uminho.pt/home/ 

rec_humanos/mostra_curriculum.php3?pessoa=12&&menu=5&&idcategoria=l) 
[6] Gianaroli L, Magli MC, Ferraretti AP, et al. (December 2008). "Birefringence characteristics in sperm heads allow for the selection of reacted 

spermatozoa for intracytoplasmic sperm injection". Fertil. Steril. doi:10.1016/j.fertnstert.2008.10.024. PMID 19064263. 
[7] Born M, and Wolf E, Principles of Optics, 7th Ed. 1999 (Cambridge University Press), §15.3.3 
[8] http://www.youtube.com/watch?v=BEClYQbuG7U 
[9] http://www.campoly.com/application_notes.html 



Polarization spectroscopy 79 



Polarization spectroscopy 



Polarization spectroscopy comprises a set of spectroscopic techniques based on polarization properties of light (not 
necessarily visible one; UV, X-ray, infrared, or in any other frequency range of the electromagnetic radiation). By 
analyzing the polarization properties of light, decisions can be made about the media that emitted the light (or the 
media the light passes/scatters through). Alternatively, a source of polarized light may be used to probe a media; in 
this case, the changes in the light polarization (comparing to the incidental one) allow to infer the media properties. 

In general, any kind of anisotropy in the media results in some sort of light polarization. Such an anisotropy can be 
either inherent to the media (e.g., in the case of a crystal substance), or imposed externally (e.g., in the presence of 
magnetic field in plasma). 

See also: 

• Zeeman effect 

• Faraday effect 

• Stark effect 

• Plasma diagnostics 



Polarized IR Spectroscopy 



Infrared spectroscopy (IR spectroscopy) is the subset of spectroscopy that deals with the infrared region of the 
electromagnetic spectrum. It covers a range of techniques, the most common being a form of absorption 
spectroscopy. As with all spectroscopic techniques, it can be used to identify compounds and investigate sample 
composition. A common laboratory instrument that uses this technique is an infrared spectrophotometer. 

The infrared portion of the electromagnetic spectrum is usually divided into three regions; the near-, mid- and far- 
infrared, named for their relation to the visible spectrum. The far-infrared, approximately 400—10 cm" 
(1000—30 |im), lying adjacent to the microwave region, has low energy and may be used for rotational spectroscopy. 
The mid-infrared, approximately 4000—400 cm - (30—2.5 u,m) may be used to study the fundamental vibrations and 
associated rotational-vibrational structure. The higher energy near-IR, approximately 14000—4000 cm" 
(2.5—0.8 |im) can excite overtone or harmonic vibrations. The names and classifications of these subregions are 
merely conventions. They are neither strict divisions nor based on exact molecular or electromagnetic properties. 

Theory 

Infrared spectroscopy exploits the fact that molecules absorb specific frequencies that are characteristic of their 
structure. These absorptions are resonant frequencies, i.e. the frequency of the absorbed radiation matches the 
frequency of the bond or group that vibrates. The energies are determined by the shape of the molecular potential 
energy surfaces, the masses of the atoms, and the associated vibronic coupling. 

In particular, in the Born— Oppenheimer and harmonic approximations, i.e. when the molecular Hamiltonian 
corresponding to the electronic ground state can be approximated by a harmonic oscillator in the neighborhood of the 
equilibrium molecular geometry, the resonant frequencies are determined by the normal modes corresponding to the 
molecular electronic ground state potential energy surface. Nevertheless, the resonant frequencies can be in a first 
approach related to the strength of the bond, and the mass of the atoms at either end of it. Thus, the frequency of the 
vibrations can be associated with a particular bond type. 



Polarized IR Spectroscopy 



80 



Number of vibrational modes 

In order for a vibrational mode in a molecule to be "IR active," it must be associated with changes in the permanent 
dipole. 

A molecule can vibrate in many ways, and each way is called a vibrational mode. Linear molecules have 3N-5 
degrees of vibrational modes whereas nonlinear molecules have 3N-6 degrees of vibrational modes (also called 
vibrational degrees of freedom). As an example HO, a non-linear molecule, will have 3*3-6 = 3 degrees of 
vibrational freedom, or modes. 

Simple diatomic molecules have only one bond and only one vibrational band. If the molecule is symmetrical, e.g. 
N2, the band is not observed in the IR spectrum, but only in the Raman spectrum. Unsymmetrical diatomic 
molecules, e.g. CO, absorb in the IR spectrum. More complex molecules have many bonds, and their vibrational 
spectra are correspondingly more complex, i.e. big molecules have many peaks in their IR spectra. 

The atoms in a CH group, commonly found in organic compounds can vibrate in six different ways: symmetrical 
and antisymmetrical stretching, scissoring, rocking, wagging and twisting: 



Symmetrical 
stretching 


Antisymmetrical 
stretching 


Scissoring 


Rocking 


Wagging 


Twisting 


V 




K? 

- V 


K? 

- V 


V 


V 



Special effects 

The simplest and most important IR bands arise from the "normal modes," the simplest distortions of the molecule. 
In some cases, "overtone bands" are observed. These bands arise from the absorption of a photon that leads to a 
doubly excited vibrational state. Such bands appear at approximately twice the energy of the normal mode. Some 
vibrations, so-called 'combination modes," involve more than one normal mode. The phenomenon of Fermi 
resonance can arise when two modes are similar in energy, Fermi resonance results in an unexpected shift in energy 
and intensity of the bands. 



Practical IR spectroscopy 

The infrared spectrum of a sample is recorded by passing a beam of infrared light through the sample. Examination 
of the transmitted light reveals how much energy was absorbed at each wavelength. This can be done with a 
monochromatic beam, which changes in wavelength over time, or by using a Fourier transform instrument to 
measure all wavelengths at once. From this, a transmittance or absorbance spectrum can be produced, showing at 
which IR wavelengths the sample absorbs. Analysis of these absorption characteristics reveals details about the 
molecular structure of the sample. When the frequency of the IR is the same as the vibrational frequency of a bond, 
absorption occurs. 

This technique works almost exclusively on samples with covalent bonds. Simple spectra are obtained from samples 
with few IR active bonds and high levels of purity. More complex molecular structures lead to more absorption 
bands and more complex spectra. The technique has been used for the characterization of very complex mixtures. 



Polarized IR Spectroscopy 



81 



Sample preparation 

Gaseous samples require a sample cell with a long pathlength (typically 5—10 cm), to compensate for the diluteness. 

Liquid samples can be sandwiched between two plates of a salt (commonly sodium chloride, or common salt, 
although a number of other salts such as potassium bromide or calcium fluoride are also used). The plates are 
transparent to the infrared light and do not introduce any lines onto the spectra. 

Solid samples can be prepared in a variety of ways. One common method is to crush the sample with an oily mulling 
agent (usually Nujol) in a marble or agate mortar, with a pestle. A thin film of the mull is smeared onto salt plates 
and measured. The second method is to grind a quantity of the sample with a specially purified salt (usually 
potassium bromide) finely (to remove scattering effects from large crystals). This powder mixture is then pressed in 
a mechanical die press to form a translucent pellet through which the beam of the spectrometer can pass. A third 
technique is the "cast film" technique, which is used mainly for polymeric materials. The sample is first dissolved in 
a suitable, non hygroscopic solvent. A drop of this solution is deposited on surface of KBr or NaCl cell. The solution 
is then evaporated to dryness and the film formed on the cell is analysed directly. Care is important to ensure that the 
film is not too thick otherwise light cannot pass through. This technique is suitable for qualitative analysis. The final 
method is to use microtomy to cut a thin (20—100 micrometre) film from a solid sample. This is one of the most 
important ways of analysing failed plastic products for example because the integrity of the solid is preserved. 

It is important to note that spectra obtained from different sample preparation methods will look slightly different 
from each other due to differences in the samples' physical states. 



Conventional apparatus 

A beam of infrared light is produced 
and split into two separate beams. One 
is passed through the sample, the other 
passed through a reference which is 
often the substance the sample is 
dissolved in. The beams are both 
reflected back towards a detector, 
however first they pass through a 
splitter which quickly alternates which 
of the two beams enters the detector. 
The two signals are then compared and 
a printout is obtained. 






IR 
source 




Processor 


Printout 



Typical apparatus 



A reference prevents fluctuations in the output of the source affecting the data. The reference also allows the effects 
of the solvent to be cancelled out (the reference is usually a pure form of the solvent the sample is in) 



FT-IR method 

Fourier transform infrared (FTIR) spectroscopy is a measurement technique for collecting infrared spectra. 
Instead of recording the amount of energy absorbed when the frequency of the infra-red light is varied 
(monochromator), the IR light is guided through an interferometer. After passing through the sample, the measured 
signal is the interferogram. Performing a Fourier transform on this signal data results in a spectrum identical to that 
from conventional (dispersive) infrared spectroscopy. 

FTIR spectrometers are cheaper than conventional spectrometers because building an interferometer is easier than 
the fabrication of a monochromator. In addition, measurement of a single spectrum is faster for the FTIR technique 
because the information at all frequencies is collected simultaneously. This allows multiple samples to be collected 
and averaged together resulting in an improvement in sensitivity. Virtually all modern infrared spectrometers are 



Polarized IR Spectroscopy 82 

FTIR instruments. 

Absorptions bands 



Wavenumbers listed in cm . 

Uses and applications 

Infrared spectroscopy is widely used in both research and industry as a simple and reliable technique for 
measurement, quality control and dynamic measurement. It is of especial use in forensic analysis in both criminal 
and civil cases, enabling identification of polymer degradation for example. 

The instruments are now small, and can be transported, even for use in field trials. With increasing technology in 
computer filtering and manipulation of the results, samples in solution can now be measured accurately (water 
produces a broad absorbance across the range of interest, and thus renders the spectra unreadable without this 
computer treatment). Some instruments will also automatically tell you what substance is being measured from a 
store of thousands of reference spectra held in storage. 

By measuring at a specific frequency over time, changes in the character or quantity of a particular bond can be 
measured. This is especially useful in measuring the degree of polymerization in polymer manufacture. Modern 
research instruments can take infrared measurements across the whole range of interest as frequently as 32 times a 
second. This can be done whilst simultaneous measurements are made using other techniques. This makes the 
observations of chemical reactions and processes quicker and more accurate. 

Techniques have been developed to assess the quality of tea-leaves using infrared spectroscopy. This will mean that 
highly trained experts (also called 'noses') can be used more sparingly, at a significant cost saving. 

Infrared spectroscopy has been highly successful for applications in both organic and inorganic chemistry. Infrared 
spectroscopy has also been successfully utilized in the field of semiconductor microelectronics : for example, 
infrared spectroscopy can be applied to semiconductors like silicon, gallium arsenide, gallium nitride, zinc selenide, 
amorphous silicon, silicon nitride, etc. 

Isotope effects 

The different isotopes in a particular species may give fine detail in infrared spectroscopy. For example, the 0-0 
stretching frequency (in reciprocal centimeters) of oxyhemocyanin is experimentally determined to be 832 and 
788 cm - for v( O- O) and v( O- O) respectively. 

By considering the 0-0 as a spring, the wavenumber of absorbance, v can be calculated: 

1 



2ttc v fi 
where k is the spring constant for the bond, c is the speed of light, and j.i is the reduced mass of the A-B system: 

m A m B 

t*= 

m,A + rug 

( TTli is the mass of atom { ). 

\f\ \f\ 1 R 18 

The reduced masses for O- O and O- O can be approximated as 8 and 9 respectively. Thus 



Polarized IR Spectroscopy 



83 




^ 1B o _ 

I/1B 

Where v is the wavenumber [wavenumber = frequency/( speed of light)] 

The effect of isotopes, both on the vibration and the decay dynamics, has been found to be stronger than previously 
thought. In some systems, such as silicon and germanium, the decay of the anti-symmetric stretch mode of interstitial 
oxygen involves the symmetric stretch mode with a strong isotope dependence. For example, it was shown that for a 
natural silicon sample, the lifetime of the anti-symmetric vibration is 1 1.4 ps. When the isotope of one of the silicon 
atoms is increased to 29Si, the lifetime increases to 19 ps, similarly, when the silicon atom is changed to 30Si, the 
lifetime becomes 27 ps 



[4] 



Two-dimensional IR 

Two-dimensional infrared correlation spectroscopy analysis is the application of 2D correlation analysis on 
infrared spectra. By extending the spectral information of a perturbed sample, spectral analysis is simplified and 
resolution is enhanced. The 2D synchronous and 2D asynchronous spectra represent a graphical overview of the 
spectral changes due to a perturbation (such as a changing concentration or changing temperature) as well as the 
relationship between the spectral changes at two different wavenumbers. 

Nonlinear two-dimensional infrared 

spectroscopy is the infrared version of 

correlation spectroscopy. Nonlinear 

two-dimensional infrared spectroscopy is a 

technique that has become available with the 

development of femtosecond infrared laser 

pulses. In this experiment first a set of pump 

pulses are applied to the sample. This is 

followed by a waiting time, where the 

system is allowed to relax. The waiting time 

typically lasts from zero to several 

picoseconds and the duration can be 

controlled with a resolution of tens of 

femtoseconds. A probe pulse is then applied 

resulting in the emission of a signal from the sample. The nonlinear two-dimensional infrared spectrum is a 

two-dimensional correlation plot of the frequency U)\ that was excited by the initial pump pulses and the frequency 

Cl^3 excited by the probe pulse after the waiting time. This allows the observation of coupling between different 

vibrational modes; because of its extremely high time resolution it can be used to monitor molecular dynamics on a 

picosecond timescale. It is still a largely unexplored technique and is becoming increasingly popular for fundamental 

research. 




time 

Pulse Sequence used to obtain a two-dimensional Fourier transform infrared 

spectrum. The time period T\ is usually referred to as the coherence time and the 

second time period 7~2 is known as the waiting time. The excitation frequency is 

obtained by Fourier transforming along the T\ axis. 



Like in two-dimensional nuclear magnetic resonance (2DNMR) spectroscopy this technique spreads the spectrum in 
two dimensions and allow for the observation of cross peaks that contain information on the coupling between 
different modes. In contrast to 2DNMR nonlinear two-dimensional infrared spectroscopy also involve the excitation 
to overtones. These excitations result in excited state absorption peaks located below the diagonal and cross peaks. In 
2DNMR two distinct techniques, COSY and NOESY, are frequently used. The cross peaks in the first are related to 
the scalar coupling, while in the later they are related to the spin transfer between different nuclei. In nonlinear 
two-dimensional infrared spectroscopy analogs have been drawn to these 2DNMR techniques. Nonlinear 
two-dimensional infrared spectroscopy with zero waiting time corresponds to COSY and nonlinear two-dimensional 
infrared spectroscopy with finite waiting time allowing vibrational population transfer corresponds to NOESY. The 



Polarized IR Spectroscopy 



84 



COSY variant of nonlinear two-dimensional infrared spectroscopy has been used for determination of the secondary 
structure content proteins. 



See also 



• Infrared spectroscopy correlation table 

• Fourier transform spectroscopy 

• Near infrared spectroscopy 

• Vibrational spectroscopy 

• Rotational spectroscopy 



Time-resolved spectroscopy 
Spectroscopy 
Quantum vibration 
Raman spectroscopy 
Infrared microscopy 
Photothermal microspectroscopy 



Polymer degradation 
Infrared astronomy 
Far infrared astronomy 
Forensic chemistry 
Forensic engineering 
Forensic polymer 
engineering 
Forensic science 
Applied spectroscopy 



External links 

• A useful gif animation of different vibrational modes: here 



[8] 



Infrared spectroscopy for organic chemists 
Organic compounds spectrum database 



[91 



References 

[1] Laurence M. Harwood, Christopher J. Moody. Experimental organic chemistry: Principles and Practice (Illustrated edition ed.). pp. 292. 
[2] Luypaert, J.; Zhang, M.H.; Massart, D.L. (2003), "Feasibility study for the use of near infrared spectroscopy in the qualitative and 

quantitative analysis of green tea, Camellia sinensis (L.)", Analytica Chimica Acta, 478(2), Elsevier, pp. 303—312 
[3] Lau, W.S. (1999). Infrared characterization for microelectronics. World Scientific. 
[4] Isotope Dependence of the Lifetime of the 1136-cm[sup -1] Vibration of Oxygen in Silicon K. K. Kohli, Gordon Davies, N. Q. Vinh, D. 

West, S. K. Estreicher, T. Gregorkiewicz, I. Izeddin, and K. M. Itoh, Phys. Rev. Lett. 96, 225503 (2006), 

DOI:10.1103/PhysRevLett.96.225503 
[5] P. Hamm, M. H. Lim, R. M. Hochstrasser (1998). "Structure of the amide I band of peptides measured by femtosecond nonlinear-infrared 

spectroscopy". J. Phys. Chem. B 102: 6123. doi:10.1021/jp9813286. 
[6] S. Mukamel (2000). "Multidimensional Fentosecond Correlation Spectroscopies of Electronic and Vibrational Excitations". Annual Review of 

Physics and Chemistry 51: 691. doi:10.1146/annurev.physchem. 51. 1.691. 
[7] N. Demirdoven, C. M. Cheatum, H. S. Chung, M. Khalil, J. Knoester, A. Tokmakoff (2004). "Two-dimensional infrared spectroscopy of 

antiparallel beta-sheet secondary structure". Journal of the American Chemical Society 126: 7981. doi: 10.1021/ja04981 lj. 
[8] http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/irspecl.htm 
[9] http : // w w w . organic world wide, net/infrared 
[10] http://riodb01.ibase.aist.go.jp/sdbs/cgi-bin/cre_index.cgi?lang=eng 



Circular dichroism 



85 



Circular dichroism 



First pioneered by Jean-Baptiste Biot, Augustin Fresnel, and Aime Cotton 

[2] [3] 



[1] 



circular dichroism (CD) refers to the 
differential absorption of left and right circularly polarized light. L ^ J L ' J . This phenomenon is exhibited in the 
absorption bands of optically active chiral molecules. CD spectroscopy has a wide range of applications in many 
different fields. Most notably, UV CD is used to investigate the secondary structure of proteins . UV/Vis CD is 
used to investigate charge-transfer transitions . Near-infrared CD is used to investigate geometric and electronic 
structure by probing metal d— >d transitions . Vibrational circular dichroism, which uses light from the infrared 
energy region, is used for structural studies of small organic molecules, and most recently proteins and DNA . 



Physical Principles 



Circular polarization of light 

Electromagnetic radiation consists of an electric and magnetic field that oscillate perpendicular to one another and to 

ro] 

the propagating direction . While linearly polarized light occurs when the electric field vector oscillates only in 
one plane and changes in magnitude, circularly polarized light occurs when the electric field vector rotates about its 
propagation direction and retains constant magnitude. Hence, it forms a helix in space while propagating. For left 
circularly polarized light (LCP) with propagation towards the observer, the electric vector rotates counterclockwise 
. For right circularly polarized light (RCP), the electric vector rotates clockwise. 



[9] 



Linearly polarized 



Circularly polari; 




Interaction of circularly polarized light with matter 

When circularly polarized light passes through an absorbing optically active medium, the speeds between right and 

left polarizations differ (c * c ) as well as their wavelength (X * X ) and the extent to which they are absorbed 

rioi 

(e *e ). Circular dichroism is the difference Ae = e T - e_ . The electric field of a light beam causes a linear 

L R L R 

displacement of charge when interacting with a molecule (electric dipole), whereas the magnetic field of it causes a 
circulation of charge (magnetic dipole). These two motions combined cause an excitation of an electron in a helical 
motion, which includes translation and rotation and their associated operators. The experimentally determined 
relationship between the rotational strength (R) of a sample and the As is given by 



R 



3hcl0 3 ln(10) 



c.rp 



— dv 

v 



32n 3 N A 
The rotational strength has also been determined theoretically, 



Circular dichroism 86 






We see from these two equations that in order to have non-zero /\^ , the electric and magnetic dipole moment 
operators ( M( i a- i \ an d Mi j i \) must transform as the same irreducible representation. C* n and D n 

are the only point groups where this can occur, making only chiral molecules CD active. 

Simply put, since circularly polarized light itself is "chiral", it interacts differently with chiral molecules. That is, the 
two types of circularly polarized light are absorbed to different extents. In a CD experiment, equal amounts of left 
and right circularly polarized light of a selected wavelength are alternately radiated into a (chiral) sample. One of the 
two polarizations is absorbed more than the other one, and this wavelength-dependent difference of absorption is 
measured, yielding the CD spectrum of the sample. Due to the interaction with the molecule, the electric field vector 
of the light traces out an elliptical path after passing through the sample. 

Delta absorbance 

By definition, 

AA = A L - A R 

where AA (Delta Absorbance) is the difference between absorbance of left circularly polarized (LCP) and right 
circularly polarized (RCP) light (this is what is usually measured). AA is a function of wavelength, so for a 
measurement to be meaningful the wavelength it was performed at must be known. 

Molar circular dichroism 

It can also be expressed, by applying Beer's law, as: 

AA = (e L -e R )Cl 
where 

e and e are the molar extinction coefficients for LCP and RCP light, 

C is the molar concentration 

/ is the path length in centimeters (cm). 
Then 

Ae = e L - e R 
is the molar circular dichroism. This intrinsic property is what is usually meant by the circular dichroism of the 
substance. Since /\^ is a function of wavelength, a molar circular dichroism value ( /\^ ) must specify the 
wavelength at which it is valid. 

Extrinsic effects on circular dichroism 

In many practical applications of circular dichroism (CD), as discussed below, the measured CD is not simply an 
intrinsic property of the molecule, but rather depends on the molecular conformation. In such a case the CD may also 
be a function of temperature, concentration, and the chemical environment, including solvents. In this case the 
reported CD value must also specify these other relevant factors in order to be meaningful. 

Molar ellipticity 

Although AA is usually measured, for historical reasons most measurements are reported in degrees of ellipticity. 
Molar circular dichroism and molar ellipticity, [9], are readily interconverted by the equation: 



Circular dichroism 



87 




Elliptical polarized light (purple) is composed of 

unequal contributions of right (blue) and left (red) 

circular polarized light. 



[B] = 3298.2 Ae. 

This relationship is derived by defining the ellipticity of the polarization as: 

Er — E L 



tan# = 



E R + E L 



where 



E and E are the magnitudes of the electric field vectors of the right-circularly and left-circularly polarized 

R Ij 

light, respectively. 
When E equals E (when there is no difference in the absorbance of right- and left -circular polarized light), 6 is 0° 

R L 

and the light is linearly polarized. When either E or E is equal to zero (when there is complete absorbance of the 

R L 

circular polarized light in one direction), 6 is 45° and the light is circularly polarized. 

Generally, the circular dichroism effect is small, so tanB is small and can be approximated as 6 in radians. Since the 
intensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes: 

, ,-1/2 r 1 ^ 
# (radians) 



(j? - ff) 



Then by substituting for I using Beer's law in natural logarithm form: 

I = I e- M0 
The ellipticity can now be written as: 



6> (radians) 



(e 1 



-In 10 



lnlON 



e 2 



1 



^lnlO 



fLlnlO> 



,AA± 



(e^ Inl0 + e^ lnl °) e^HT + 1 
Since A A « 1, this expression can be approximated by expanding the exponentials in a Taylor series to first-order 
and then discarding terms of AA in comparison with unity and converting from radians to degrees: 

'lnl0\ /180 x 



# (degrees) = A A 



4 j \ n 
The linear dependence of solute concentration and pathlength is removed by defining molar ellipticity as, 

H = — 

L J CI 
Then combining the last two expression with Beer's law, molar ellipticity becomes: 



Circular dichroism 



= mAe (^\m\ = 3298.2 A, 



\ 4 y \ 7r / 

Mean residue ellipticity 

Methods for estimating secondary structure in polymers, proteins and polypeptides in particular, often require that 
the measured molar ellipticity spectrum be converted to a normalized value, specifically a value independent of the 
polymer length. Mean residue ellipticity is used for this purpose; it is simply the measured molar ellipticity of the 
molecule divided by the number of monomer units (residues) in the molecule. 

Application to biological molecules 

In general, this phenomenon will be exhibited in absorption bands of any optically active molecule. As a 
consequence, circular dichroism is exhibited by biological molecules, because of their dextrorotary and levorotary 
components. Even more important is that a secondary structure will also impart a distinct CD to its respective 
molecules. Therefore, the alpha helix of proteins and the double helix of nucleic acids have CD spectral signatures 
representative of their structures. 

CD is closely related to the optical rotatory dispersion (ORD) technique, and is generally considered to be more 
advanced. CD is measured in or near the absorption bands of the molecule of interest, while ORD can be measured 
far from these bands. CD's advantage is apparent in the data analysis. Structural elements are more clearly 
distinguished since their recorded bands do not overlap extensively at particular wavelengths as they do in ORD. In 
principle these two spectral measurements can be interconverted through an integral transform (Kramers— Kronig 
relation), if all the absorptions are included in the measurements. 

The far-UV (ultraviolet) CD spectrum of proteins can reveal important characteristics of their secondary structure. 
CD spectra can be readily used to estimate the fraction of a molecule that is in the alpha-helix conformation, the 
beta-sheet conformation, the beta-turn conformation, or some other (e.g. random coil) conformation. These 

fractional assignments place important constraints on the possible secondary conformations that the protein can be 
in. CD cannot, in general, say where the alpha helices that are detected are located within the molecule or even 
completely predict how many there are. Despite this, CD is a valuable tool, especially for showing changes in 
conformation. It can, for instance, be used to study how the secondary structure of a molecule changes as a function 
of temperature or of the concentration of denaturing agents, e.g. Guanidinium hydrochloride or urea. In this way it 
can reveal important thermodynamic information about the molecule (such as the enthalpy and Gibbs free energy of 
denaturation) that cannot otherwise be easily obtained. Anyone attempting to study a protein will find CD a valuable 
tool for verifying that the protein is in its native conformation before undertaking extensive and/or expensive 
experiments with it. Also, there are a number of other uses for CD spectroscopy in protein chemistry not related to 
alpha-helix fraction estimation. 

The near-UV CD spectrum (>250 nm) of proteins provides information on the tertiary structure. The signals obtained 
in the 250-300 nm region are due to the absorption, dipole orientation and the nature of the surrounding environment 
of the phenylalanine, tyrosine, cysteine (or S-S disulfide bridges) and tryptophan amino acids. Unlike in far-UV CD, 
the near-UV CD spectrum cannot be assigned to any particular 3D structure. Rather, near-UV CD spectra provide 
structural information on the nature of the prosthetic groups in proteins, e.g., the heme groups in hemoglobin and 
cytochrome c. 

Visible CD spectroscopy is a very powerful technique to study metal— protein interactions and can resolve individual 
d-d electronic transitions as separate bands. CD spectra in the visible light region are only produced when a metal 
ion is in a chiral environment, thus, free metal ions in solution are not detected. This has the advantage of only 
observing the protein-bound metal, so pH dependence and stoichiometrics are readily obtained. Optical activity in 
transition metal ion complexes have been attributed to configurational, conformational and the vicinal effects. 
Klewpatinond and Viles (2007) have produced a set of empirical rules for predicting the appearance of visible CD 



Circular dichroism 

spectra for Cu and Ni square-planar complexes involving histidine and main-chain coordination. 

CD gives less specific structural information than X-ray crystallography and protein NMR spectroscopy, for 
example, which both give atomic resolution data. However, CD spectroscopy is a quick method that does not require 
large amounts of proteins or extensive data processing. Thus CD can be used to survey a large number of solvent 
conditions, varying temperature, pH, salinity, and the presence of various cofactors. 

CD spectroscopy is usually used to study proteins in solution, and thus it complements methods that study the solid 
state. This is also a limitation, in that many proteins are embedded in membranes in their native state, and solutions 
containing membrane structures are often strongly scattering. CD is sometimes measured in thin films. 

Experimental limitations 

CD has also been studied in carbohydrates, but with limited success due to the experimental difficulties associated 
with measurement of CD spectra in the vacuum ultraviolet (VUV) region of the spectrum (100-200 nm), where the 
corresponding CD bands of unsubstituted carbohydrates lie. Substituted carbohydrates with bands above the VUV 
region have been successfully measured. 

Measurement of CD is also complicated by the fact that typical aqueous buffer systems often absorb in the range 
where structural features exhibit differential absorption of circularly polarized light. Phosphate, sulfate, carbonate, 
and acetate buffers are generally incompatible with CD unless made extremely dilute e.g. in the 10-50 mM range. 
The TRIS buffer system should be completely avoided when performing far-UV CD. Borate and Onium compounds 
are often used to establish the appropriate pH range for CD experiments. Some experimenters have substituted 
fluoride for chloride ion because fluoride absorbs less in the far UV, and some have worked in pure water. Another, 
almost universal, technique is to minimize solvent absorption by using shorter path length cells when working in the 
far UV, 0. 1 mm path lengths are not uncommon in this work. 

In addition to measuring in aqueous systems, CD, particularly far-UV CD, can be measured in organic solvents e.g. 
ethanol, methanol, trifluoroethanol (TFE). The latter has the advantage to induce structure formation of proteins, 
inducing beta-sheets in some and alpha helices in others, which they would not show under normal aqueous 
conditions. Most common organic solvents such as acetonitrile, THF, chloroform, dichloromethane are however, 
incompatible with far-UV CD. 

It may be of interest to note that the protein CD spectra used in secondary structure estimation are related to the n to 
jt*orbital absorptions of the amide bonds linking the amino acids. These absorption bands lie partly in the so-called 
vacuum ultraviolet (wavelengths less than about 200 nm). The wavelength region of interest is actually inaccessible 
in air because of the strong absorption of light by oxygen at these wavelengths. In practice these spectra are 
measured not in vacuum but in an oxygen-free instrument (filled with pure nitrogen gas). 

Once oxygen has been eliminated, perhaps the second most important technical factor in working below 200 nm is to 
design the rest of the optical system to have low losses in this region. Critical in this regard is the use of aluminized 
mirrors whose coatings have been optimized for low loss in this region of the spectrum. 

The usual light source in these instruments is a high pressure, short-arc xenon lamp. Ordinary xenon arc lamps are 
unsuitable for use in the low UV. Instead, specially constructed lamps with envelopes made from high-purity 
synthetic fused silica must be used. 

Light from synchrotron sources has a much higher flux at short wavelengths, and has been used to record CD down 
to 160 nm. Recently the CD spectrometer at the electron storage ring facility ISA at the University of Aarhus in 
Denmark was used to record solid state CD spectra down to 120 nm. 

At the quantum mechanical level, the information content of circular dichroism and optical rotation are identical. 



Circular dichroism 90 

See also 

• Circular polarization in nature 

• Dichroism 

• Linear dichroism 

• Magnetic circular dichroism 

• Optical activity 

• Optical isomerism 

• Optical rotation 

• Optical rotatory dispersion 

Further reading 

ri3i 

1. Alison Rodger and Bengt Norden, Circular Dichroism and Linear Dichroism (1997) Oxford University 
Press, Oxford, UK. ISBN 019855897X. 

2. Fasman, G.D., Circular Dichroism and the Conformational Analysis of Biomolecules (1996) Plenum Press, New 
York. 

rd 

3. Hecht, E., Optics 3 Edition (1998) Addison Wesley Longman, Massachusetts. 

4. Klewpatinond, M. and Viles, J.H. (2007) Empirical rules for rationalising visible circular dichroism of Cu and 
Ni histidine complexes: Applications to the prion protein. FEBS Letters 581, 1430-1434. 

External links 

ri4i 

• Circular Dichroism explained 

• Circular Dichroism at UMDNJ - a good site for information on structure estimation software 

• Electromagnetic waves - Animated electromagnetic waves. The Emanim program is a teaching resource for 
helping students understand the nature of electromagnetic waves and their interaction with birefringent and 

dichroic samples 

ri7i 

• An Introduction to Circular Dichroism Spectroscopy - a very good tutorial on circular dichroism spectroscopy 

References 

[I] G. D. Fasman (1996). Plenum Press, p. 3. 

[2] P. Atkins and J. de Paula (2005). Elements of Physical Chemistry, 4th ed.. Oxford University Press. 

[3] E. I. Solomon and A. B. P. Lever (2006). 1. Wiley, p. 78. 

[4] R. W. Woody (1994). K. Nakanishi, N. Berova, R. W. Woody, ed. VCH Publishers, Inc.. p. 473. 

[5] Solomon, Neidig; A. T. Wecksler, G. Schenk, and T. R. Holman (2007). "Kinetic and Spectroscopic Studies of N694C Lipoxygenase: A 

Probe of the Substrate Activation Mechanism of a Nonheme Ferric Enzyme". JACS 129: 7531—7537. 
[6] E. I. Solomon and A. B. P. Lever (2006). 1. Wiley, p. 78. 
[7] K. Nakanishi, N. Berova, R. W. Woody, ed (1994). VCH Publishers, Inc.. 

[8] A. Rodger and B. Norden (1997). Circular Dichroism and Linear Dichroism. Oxford University Press. 
[9] E. I. Solomon and A. B. P. Lever (2006). 1. Wiley, p. 78. 
[10] Woody,R.W.1994 

[II] Whitmore L, Wallace BA (2008). "Protein secondary structure analyses from circular dichroism spectroscopy: methods and reference 
databases". Biopolymers 89 (5): 392-400. doi:10.1002/bip.20853. PMID 17896349. 

[12] Greenfield NJ (2006). "Using circular dichroism spectra to estimate protein secondary structure". Nature protocols 1 (6): 2876—90. 

doi:10.1038/nprot.2006.202. PMID 17406547. 

[13] http://books.google.co.uk/books ?hl=en&id=THeKGC99hJcC 

[14] http://www.ap-lab.com/circular_dichroism.htm 

[15] http://www2.umdnj.edU/cdrwjweb/index.htm#software 

[16] http://www.enzim.hu/~szia/cddemo/edemol.htm 

[17] http://www.photophysics.com/circulardichroism.php 



Vibrational circular dichroism 



91 



Vibrational circular dichroism 



Vibrational circular dichroism (VCD) is a spectroscopic technique which detects differences in attenuation of left 
and right circularly polarized light passing through a sample. It is basically circular dichroism spectroscopy in the 
infrared and near infrared ranges . 

Because VCD is sensitive to the mutual orientation of distinct groups in a molecule, it provides three-dimensional 
structural information. Thus, it is a powerful technique as VCD spectra of enantiomers can be simulated using ab 
initio calculations, thereby allowing the identification of absolute configurations of small molecules in solution from 
VCD spectra. Among such quantum computations of VCD spectra resulting from the chiral properties of small 
organic molecules are those based on density functional theory (DFT) and gauge-invariant atomic orbitals (GIAO). 
As a simple example of the experimental results that were obtained by VCD are the spectral data obtained within the 
carbon-hydrogen (C-H) stretching region of 21 amino acids in heavy water solutions. Measurements of vibrational 
optical activity (VOA) have thus numerous applications, not only for small molecules, but also for large and 
complex biopolymers such as muscle proteins (myosin, for example) and DNA. 



Vibrational modes 



K? 








K* 




Theory of VCD 

While the fundamental quantity associated with the infrared absorption is the dipole strength, the differential 
absorption is proportional also to the rotational strength, a quantity which depends on both the electric and magnetic 
dipole transition moments. Sensitivity of the handedness of a molecule toward circularly polarized light results from 
the form of the rotational strength. 



VCD of peptides and proteins 



Extensive VCD studies have been reported for both polypeptides and several proteins in solution ; several 

recent reviews were also compiled . An extensive but not comprehensive VCD publications list is also 

provided in the "References" section. The published reports over the last 22 years have established VCD as a 
powerful technique with improved results over those previously obtained by visible/UV circular dichroism (CD) or 
optical rotatory dispersion (ORD) for proteins and nucleic acids. 



Vibrational circular dichroism 



92 



Amino acid and polypeptide structures 






+ H,N X 








/ C pT 


-CH, 







- 


H,C- 


-\c- 




Na + 




=^*> 



Cation Zuitterion Anion 



:»fr£&** | 















Bcl-2 Family 



§=!= 






Vibrational circular dichroism 



93 




VCD of nucleic acids 

VCD spectra of nucleotides, synthetic polynucleotides and several nucleic acids, including DNA, have been reported 
and assigned in terms of the type and number of helices present in A- , B-, and Z- DNA. 



VCD Instrumentation 

For biopolymers such as proteins and nucleic acids, the difference in absorbance between the levo- and dextro- 
configurations is five orders of magnitude smaller than the corresonding (unpolarized) absorbance. Therefore, VCD 
of biopolymers requires the use of very sensitive, specially built instrumentation as well as time-averaging over 
relatively long intervals of time even with such sensitive VCD spectrometers. Most CD instruments produce left- and 
right- circularly polarized light which is then either sine-wave or square-wave modulated, with subsequent 
phase-sensitive detection and lock-in amplification of the detected signal. In the case of FT- VCD, a photo-elastic 
modulator (PEM) is employed in conjunction with an FT-IR interferometer set-up. An example is that of a Bomem 
model MB -100 FT-IR interferometer equipped with additional polarizing optics/ accessories needed for recording 
VCD spectra. A parallel beam emerges through a side port of the interferometer which passes first through a wire 
grid linear polarizer and then through an octagonal-shaped ZnSe crystal PEM which modulates the polarized beam at 
a fixed, lower frequency such as 37.5 kHz. A mechanically stressed crystal such as ZnSe exhibits birefringence when 
stressed by an adjacent piezoelectric transducer. The linear polarizer is positioned close to, and at 45 degrees, with 
respect to the ZnSe crystal axis. The polarized radiation focused onto the detector is doubly modulated, both by the 
PEM and by the interferometer setup. A very low noise detector, such as MCT (HgCdTe), is also selected for the 
VCD signal phase-sensitive detection. Quasi-complete commercial FT-VCD instruments are also available from a 
few manufacturers but these are quite expensive and also have to be still considered as being at the prototype stage. 
To prevent detector saturation an appropriate, long wave pass filter is placed before the very low noise MCT 
detector, which allows only radiation below 1750 cm - to reach the MCT detector; the latter however measures 
radiation only down to 750 cm - . FT-VCD spectra accumulation of the selected sample solution is then carried out, 
digitized and stored by an in-line computer. Published reviews that compare various VCD methods are also 



available 



[9] [10] 








n;in 





^WfM 








m. 


1 J , 


(l«™H« 


™™, - 




1 





Vibrational circular dichroism 



94 




BjNj 7759 A 
n 90.48° 




Magnetic VCD 

VCD spectra have also been reported in the presence of an applied external magnetic field 1 
enhance the VCD spectral resolution for small molecules 



[ll] 



This method can 



Raman optical activity (ROA) 



-i 



ROA is a technique complementary to VCD especially useful in the 50 — 1600 cm spectral region; it is considered 
as the technique of choice for determining optical activity for photon energies less than 600 cm - . 



References 



Peptides and proteins 

• Huang R, Wu L, McElheny D, Bour P, Roy A, Keiderling TA. Cross-Strand Coupling and Site-Specific 
Unfolding Thermodynamics of a Trpzip beta-Hairpin Peptide Using (13)C Isotopic Labeling and IR 
Spectroscopy. The journal of physical chemistry. B. 2009 Apr;113(16):5661-74. 

• "Vibrational Circular Dichroism of Poly alpha-Benzyl-L-Glutamate," R. D. Singh, and T. A. Keiderling, 
Biopolymers, 20, 237-40 (1981). 

• "Vibrational Circular Dichroism of Polypeptides II. Solution Amide II and Deuteration Results," A. C. Sen and T. 
A. Keiderling, Biopolymers, 23, 1519-32 (1984). 

• "Vibrational Circular Dichroism of Polypeptides III. Film Studies of Several alpha-Helical and 6-Sheet 
Polypeptides," A. C. Sen and T. A. Keiderling, Biopolymers, 23, 1533-46 (1984). 

• "Vibrational Circular Dichroism of Polypeptides IV. Film Studies of L-Alanine Homo Oligopeptides," U. 
Narayanan, T. A. Keiderling, G. M. Bonora, and C. Toniolo, Biopolymers 24, 1257-63 (1985). 

• "Vibrational Circular Dichroism of Polypeptides, T. A. Keiderling, S. C. Yasui, A. C. Sen, C. Toniolo, G. M. 
Bonora, in Peptides Structure and Function, Proceedings of the 9th American Peptide Symposium," ed. C. M. 
Deber, K. Kopple, V. Hruby; Pie rce Chemical: Rockford, IL; 167-172 (1985). 

• "Vibrational Circular Dichroism of Polypeptides V. A Study of 310 Helical-Octapeptides" S. C. Yasui, T. A. 
Keiderling, G M. Bonora, C. Toniolo, Biopolymers 25, 79-89 (1986). 

• "Vibrational Circular Dichroism of Polypeptides VI. Polytyrosine alpha-helical and Random Coil Results," S. C. 
Yasui and T. A. Keiderling, Biopolymers 25, 5-15 (1986). 

• "Vibrational Circular Dichroism of Polypeptides VII. Film and Solution Studies of alpha-forming 
Homo-Oligopeptides," U. Narayanan, T. A. Keiderling, G M. Bonora, C. Toniolo, Journal of the American 
Chemical Society, 108, 2431-2437 (1986). 

• "Vibrational Circular Dichroism of Polypeptides VIII. Poly Lysine Conformations as a Function of pH in 
Aqueous Solution," S. C. Yasui, T. A. Keiderling, Journal of the American Chemical Society, 108, 5576-5581 
(1986). 

• "Vibrational Circular Dichroism of Polypeptides IX. A Study of Chain Length Dependence for 3 10-Helix 
Formation in Solution." S. C. Yasui, T. A. Keiderling, F. Formaggio, G M. Bonora, C. Toniolo, Journal of the 
American Chemical Society 108, 4988-499 3 (1986). 

• "Vibrational Circular Dichroism of Biopolymers." T. A. Keiderling, Nature, 322, 851-852 (1986). 



Vibrational circular dichroism 95 

• "Vibrational Circular Dichroism of Polypeptides X. A Study of alpha-Helical Oligopeptides in Solution." S. C. 
Yasui, T. A. Keiderling, R. Katachai, Biopolymers 26, 1407-1412 (1987). 

• "Vibrational Circular Dichroism of Polypeptides XL Conformation of 

Poly (L-Ly sine(Z)-L-Lysine(Z)-L- 1 -Pyrenylalanine) and Poly (L-Lysine(Z)-L-Ly sine(Z)-L- 1 -Napthylala-nine) in 
Solution" S. C. Yasui, T. A. Keiderling, and M. Sisido, Macromolecules 20, 2 403-2406 (1987). 

• "Vibrational Circular Dichroism of Biopolymers" T. A. Keiderling, S. C. Yasui, A. C. Sen, U. Narayanan, A. 
Annamalai, P. Malon, R. Kobrinskaya, L. Yang, in "F.E.C.S. Second International Conference on Circular 
Dichroism, Conference Proceedings," ed. M. Kajtar, L. Eotvos Univ., Budapest, 1987, p. 155-161. 

• "Vibrational Circular Dichroism of Poly-L-Proline and Other Helical Poly-peptides," R. Kobrinskaya, S. C. 
Yasui, T. A. Keiderling, in "Peptides: Chemistry and Biology, Proceedings of the 10th American Peptide 
Symposium," ed. G. R. Marshall, ESCOM, L eiden, 1988, p. 65-67. 

• "Vibrational Circular Dichroism of Polypeptides with Aromatic Side Chains," S. C. Yasui, T. A. Keiderling, in 
"Peptides: Chemistry and Biology, Proceedings of the 10th American Peptide Symposium," ed. G. R. Marshall, 
ESCOM, Leiden, 1988, p. 90-92. 

• "Vibrational Circular Dichroism of Polypeptides XII. Re-evaluation of the Fourier Transform Vibrational Circular 
Dichroism of Poly-gamma-Benzyl-L-Glutamate," P. Malon, R. Kobrinskaya, T. A. Keiderling, Biopolymers 27, 
733-746 (1988). 

• "Vibrational Circular Dichroism of Biopolymers," T. A. Keiderling, S. C. Yasui, U. Narayanan, A. Annamalai, P. 
Malon, R. Kobrinskaya, L. Yang, in Spectroscopy of Biological Molecules New Advances ed. E. D. Schmid, F. W. 
Schneider, F. Siebert, p. 73-76 (1988). 

• "Vibrational Circular Dichroism of Polypeptides and Proteins," S. C. Yasui, T. A. Keiderling, Mikrochimica Acta, 
II, 325-327, (1988). 

• "(lR,7R)-7-Methyl-6,9, -Diazatricyclo[6, 3,0,01, 6]Tridecanne-5,10-Dione, A Tricyclic Spirodilactam Containing 
Non-planar Amide Groups: Synthesis, NMR, Crystal Structure, Absolute Configuration, Electronic and 
Vibrational Circular Dichroism" P. Malon, C . L. Barness, M. Budesinsky, R. K. Dukor, D. van der Helm, T. A. 
Keiderling, Z. Koblicova, F. Pavlikova, M. Tichy, K. Blaha, Collections of Czechoslovak Chemical 
Communications 53, 2447-2472 (1988). 

• "Vibrational Circular Dichroism of Poly Glutamic Acid" R. K. Dukor, T. A. Keiderling, in Peptides 1988 (ed. G 
Jung, E. Bayer) Walter de Gruyter, Berlin (1989) pp 519-521. 

• "Biopolymer Conformational Studies with Vibrational Circular Dichroism" T. A. Keiderling, S. C. Yasui, P. 
Pancoska, R. K. Dukor, L. Yang, SPIE Proceeding 1057, ("Biomolecular Spectroscopy," ed. H. H. Mantsch, R. R. 
Birge) 7-14 (1989). 

• "Vibrational Circular Dichroism. Comparison of Techniques and Practical Considerations" T. A. Keiderling, in 
"Practical Fourier Transform Infrared Spectroscopy. Industrial and Laboratory Chemical Analysis," ed. J. R. 
Ferraro, K. Krishnan (Academic Press, San Diego, 1990) p. 203-284. 

• "Vibrational Circular Dichroism Study of Unblocked Proline Oligomers," R. K. Dukor, T. A. Keiderling, V. Gut, 
International Journal of Peptide and Protein Research, 38, 198-203 (1991). 

• "Reassessment of the Random Coil Conformation. Vibrational CD Study of Proline Oligopeptides and Related 
Polypeptides" R. K. Dukor and T. A. Keiderling, Biopolymers 31 1747-1761 (1991). 

• "Vibrational CD of the Amide II band in Some Model Polypeptides and Proteins" V. P. Gupta, T. A. Keiderling, 
Biopolymers 32 239-248 (1992). 

• "Vibrational Circular Dichroism of Proteins Polysaccharides and Nucleic Acids" T. A. Keiderling, Chapter 8 in 
Physical Chemistry of Food Processes, Vol. 2 Advanced Techniques, Structures and Applications., eds. I.C. 
Baianu, H. Pessen, T. Kumosinski, Van Norstrand — Reinhold, New York (1993), pp 307—337. 

• "Structural Studies of Biological Macromolecules using Vibrational Circular Dichroism" T. A. Keiderling, P. 
Pancoska, Chapter 6 in Advances in Spectroscopy Vol. 21, Biomolecular Spectroscopy Part B eds. R. E. Hester, 
R. J. H. Clarke, John W iley Chichester (1993) pp 267-315. 



Vibrational circular dichroism 

• "Ab Initio Simulations of the Vibrational Circular Dichroism of Coupled Peptides" P. Bour and T. A. Keiderling, 
Journal of the American Chemical Society 115 9602-9607 (1993). 

• "Ab initio Simulations of Coupled Peptide Vibrational Circular Dichroism" P. Bour, T. A. Keiderling in "Fifth 
International Conference on The Spectroscopy of Biological Molecules" Th. Theophanides, J. Anastassopoulou, 
N. Fotopoulos (Eds), Kluwen Aca demic Publ., Dortrecht, 1993, p. 29-30. 

• "Vibrational Circular Dichroism Spectroscopy of Peptides and Proteins" T. A. Keiderling, in "Circular Dichroism 
Interpretations and Applications," K. Nakanishi, N. Berova, R. Woody, Eds., VCH Publishers, New York, (1994) 
pp 497-521. 

• "Conformational Study of Sequential Lys-Leu Based Polymers and Oligomers using Vibrational and Electronic 
Circular Dichroism Spectra" V. Baumruk, D. Huo, R. K. Dukor, T. A. Keiderling, D. LeLeivre and A. Brack 
Biopolymers 34, 1115-1121 (1994). 

• "Vibrational Optical Activity of Oligopeptides" T. B. Freedman, L. A. Nafie, T. A. Keiderling Biopolymers 
(Peptide Science) 37 (ed. C. Toniolo) 265-279 (1995). 

• "Characterization of 6-bend ribbon spiral forming peptides using electronic and vibrational circular dichroism" G. 
Yoder, T. A. Keiderling, F. Formaggio, M. Crisma, C. Toniolo Biopolymers 35, 103-111 (1995). 

• "Vibrational Circular Dichroism as a Tool for Determination of Peptide Secondary Structure" P. Bour, T. A. 
Keiderling, P. Malon, in "Peptides 1994 (Proceedings of the 23rd European Peptide Symposium, 1994," (H.L.S. 
Maia, ed.), Escom, Le iden 1995, p. 517-518. 

• "Helical Screw Sense of homo-oligopeptides of C-alpha-methylated alpha-amino acids as Determined with 
Vibrational Circular Dichroism." G. Yoder, T. A. Keiderling, M. Crisma, F. Formaggio, C. Toniolo, J. Kamphuis, 
Tetrahedron Asymmetry 6, 687 -690 (1995). 

• "Conformational Study of Linear Alternating and Mixed D- and L-Proline Oligomers Using Electronic and 
Vibrational CD and Fourier Transform IR." W. M&#228stle, R. K. Dukor, G Yoder, T. A. Keiderling 
Biopolymers 36, 623-631 (1995). 

• Review: "Vibrational Circular Dichroism Applications to Conformational Analysis of Biomolecules" T. A. 
Keiderling in Circular Dichroism and the Conformational Analysis of Biomolecules ed. G D. Fasman, Plenum, 
New York (1996) p. 555-585. 

• "Mutarotation studies of Poly L-Proline using FT-IR, Electronic and Vibrational Circular Dichroism" R. K. 
Dukor, T. A. Keiderling, Biospectroscopy 2, 83-100 (1996). 

• "Vibrational Circular Dichroism Applications in Proteins and Peptides" T. A. Keiderling, Proceedings of the 
NATO ASI in Biomolecular Structure and Dynamics, Loutrakii Greece, May 1996, Ed. G Vergoten (delayed 
second volume to 1998). 

• "Transfer of Molecular Property Tensors in Cartesian Coordinates: A new algorithm for simulation of vibrational 
spectra" Petr Bour, Jana Sopkova, Lucie Bednarova, Petr Malon, T. A. Keiderling, Journal of Computational 
Chemistry 18, 6 46-659 (1997). 

• "Vibrational Circular Dichroism Characterization of Alanine-Rich Peptides." Gorm Yoder and Timothy A. 
Keiderling, "Spectroscopy of Biological Molecules: Modern Trends," Ed. P. Carmona, R. Navarro, A. Hernanz, 
Kluwer Acad. Pub., Netherlands (1997) p p. 27-28. 

• "Ionic strength effect on the thermal unfolding of alpha-spectrin peptides." D. Lusitani, N. Menhart, T.A. 
Keiderling and L. W. M. Fung. Biochemistry 37(1998)16546-16554. 

• "In search of the earliest events of hCGb folding: structural studies of the 60-87 peptide fragment" S. Sherman, L. 
Kirnarsky, O. Prakash, H. M. Rogers, R.A.G.D. Silva, T.A. Keiderling, D. Smith, A.M. Hanly, F. Perini, and 
R.W. Ruddon, American Pep tide Symposium Proceedings, 1997. 

• "Cold Denaturation Studies of (LKELPKEL)n Peptide Using Vibrational Circular Dichroism and FT-IR". R. A. 
G D. Silva, Vladimir Baumruk, Petr Pancoska, T. A. Keiderling, Eric Lacassie, and Yves Trudelle, American 
Peptide Symposium Proceedings, 1997. 



Vibrational circular dichroism 97 

• "Simulations of oligopeptide vibrational CD. Effects of isotopic labeling." Petr Bour, Jan Kubelka,T. A. 
Keiderling Biopolymers 53, 380-395 (2000). 

• "Site specific conformational determination in thermal unfolding studies of helical peptides using vibrational 
circular dichroism with isotopic substitution" R. A. G. D. Silva, Jan Kubelka, Petr Bour, Sean M. Decatur, 
Timothy A. Keiderling, Proceedings of the National Academy of Sciences (PNAS:USA) 97, 8318-8323 (2000). 

• "Folding studies on the human chorionic gonadotropin b -subunit using optical spectroscopy of peptide 
fragments" R. A. G. D. Silva, S. A. Sherman, F. Perini, E. Bedows, T. A. Keiderling, Journal of the American 
Chemical Society, 122, 8623-8630 (2000). 

• "Peptide and Protein Conformational Studies with Vibrational Circular Dichroism and Related Spectroscopies", 
Timothy A. Keiderling, (Revised and Expanded Chapter) In Circular Dichroism: Principles and Applications, 2nd 
Edition. (Eds. K. Nakanishi, N. Berova and R. A. Woody, John Wiley & Sons, New York (2000) p. 621-666. 

• "Conformation studies with Optical Spectroscopy of peptides taken from hairpin sequences in the Human 
Chorionic Gonadotropin " R. A. G D. Silva, S. A. Sherman, E. Bedows, T. A. Keiderling, Peptides for the New 
Millenium, Proceedings of the 16th American Peptide Symposium, (June, 1999 Minneapolis, MN) Ed.G B. 
Fields, J. P. Tam, G. Barany, Kluwer Acad. Pub., Dordrecht,(2000) p. 325-326. 

• "Analysis of Local Conformation within Helical Peptides via Isotope-Edited Vibrational Spectroscopy." S. M. 
Decatur, T. A. Keiderling, R. A. G D. Silva, and P. Bour, Peptides for the New Millenium, Proceedings of the 
16th American Peptide Symposium, (June, 1999 Minneapolis, MN) Ed. Ed.G. B. Fields, J. P. Tam, G Barany, 
Kluwer Acad. Pub., Dordrecht, (2000) p. 414-416. 

• "The anomalous infrared amide I intensity distribution in C-13 isotopically labeled peptide beta-sheets comes 
from extended, multiple stranded structures. An Ab Initio study." Jan Kubelka and T. A. Keiderling , Journal of 
the American Chemical Society. 123, 6142-6150 (2001). 

• "Vibrational Circular Dichroism of Peptides and Proteins: Survey of Techniques, Qualitative and Quantitative 
Analyses, and Applications" Timothy A. Keiderling, Chapter in Infrared and Raman Spectroscopy of Biological 
Materials, Ed. Bing Yan and H.-U. Gremlich, Marcel Dekker, New York (2001) p. 55-100. 

• "Chirality in peptide vibrations. Ab initio computational studies of length, solvation, hydrogen bond, dipole 
coupling and isotope effects on vibrational CD. " Jan Kubelka, Petr Bour, R. A. Gangani D. Silva, Sean M. 
Decatur, Timothy A. Keiderling, ACS Symposium Series 810, ["Chirality: Physical Chemistry," (Ed. Janice 
Hicks) American Chemical Society, Washington, DC] (2002), pp. 50—64. 

• "Spectroscopic Characterization of Selected b-Sheet Hairpin Models", J. Hilario, J. Kubelka, F. A. Syud, S. H. 
Gellman, and T. A. Keiderling. Biopolymers (Biospectroscopy) 67: 233-236 (2002) 

• " Discrimination between peptide 3 - and alpha-helices. Theoretical analysis of the impact of alpha-methyl 
substitution on experimental spectra " Jan Kubelka, R. A. Gangani D. Silva, and T. A. Keiderling, Journal of the 
American Chemical Society, 124, 5325-5332 (2002). 

• "Ab Initio Quantum Mechanical Models of Peptide Helices and their Vibrational Spectra" Petr Bour, Jan Kubelka 
and T. A. Keiderling, Biopolymers 65, 45-59 (2002). 

• "Discriminating 3 - from alpha-helices. Vibrational and electronic CD and IR Absorption study of related 
Aib-contining oligopeptides" R. A. Gangani D. Silva, Sritana Yasui, Jan Kubelka, Fernando Formaggio, Marco 
Crisma, Claudio Toniolo, and Timothy A. Keiderling, Biopolymers 65, 229-243 (2002). 

• "Spectroscopic characterization of Unfolded peptides and proteins studied with infrared absorption and 
vibrational circular dichroism spectra" T. A. Keiderling and Qi Xu, Advances in Protein Chemistry Volume 62, 
[Unfolded Proteins, Dedicated to John Edsall, Ed.: George Rose, Academic Press:New York] (2002), 

pp. 111-161. 

• "Protein and Peptide Secondary Structure and Conformational Determination with Vibrational Circular Dichroism 
" Timothy A. Keiderling, Current Opinions in Chemical Biology (Ed. Julie Leary and Mark Arnold) 6, 682-688 
(2002). 



Vibrational circular dichroism 

• Review: Conformational Studies of Peptides with Infrared Techniques. Timothy A. Keiderling and R. A. G. D. 
Silva, in Synthesis of Peptides and Pep tidomime tics, Ed. M. Goodman and G. Herrman, Houben-Weyl, Vol 22Eb, 
Georg Thiem Verlag, New York (2002) pp. 715—738, (written and accepted in 2000). 

• "Spectroscopic Studies of Structural Changes in Two beta-Sheet Forming Peptides Show an Ensemble of 
Structures That Unfold Non-Cooperatively" Serguei V. Kuznetsov, Jovencio Hilario, T. A. Keiderling, Anjum 
Ansari, Biochemistry, 42 :4321-4332, (2003). 

• "Optical spectroscopic investigations of model beta-sheet hairpins in aqueous solution" Jovencio Hilario, Jan 
Kubelka, T. A. Keiderling, Journal of the American Chemical Society 125, 7562-757 '4 (2003). 

• "Synthesis and conformational study of homopeptides based on (S)-Bin, a C2-symmetric binapthyl-derived 
Caa-disubstituted glycine with only axial chirality" J. -P. Mazaleyrat, K. Wright, A. Gaucher, M. Wakselman, S. 
Oancea, F. Formaggio, C. Toniolo, V. Setnicka, J. Kapitan, T. A. Keiderling, Tetrahedron Asymmetry, 14, 
1879-1893 (2003). 

• "Empirical modeling of the peptide amide I band IR intensity in water solution," Petr Bour, Timothy A. 
Keiderling, Journal of Chemical Physics, 119, 11253-11262 (2003) 

• "The Nature of Vibrational Coupling in Helical Peptides: An Isotope Labeling Study" by R. Huang, J. Kubelka, 
W. Barber- Armstrong, R. A. G D Silva, S. M. Decatur, and T. A. Keiderling, Journal of the American Chemical 
Society, 126, 2346-2354 (2004). 

• "The Complete Chirospectroscopic Signature of the Peptide 3 Helix in Aqueous Solution" Claudio Toniolo, 
Fernando Formaggio, Sabrina Tognon, Quirinus B. Broxterman, Bernard Kaptein, Rong Huang, Vladimir 
Setnicka, Timothy A. Keiderling, Iain H. McColl, Lutz Hecht, Laurence D. Barron, Biopolymers 75, 32-45 
(2004). 

• "Induced axial chirality in the biphenyl core for the Ca-tetrasubstituted a-amino acid residue Bip and subsequent 
propagation of chirality in (Bip)n/Val oligopeptides" J. -P. Mazaleyrat, K. Wright, A. Gaucher, N. Toulemonde, 
M. Wakselman, S. Oancea, C. Peggion, F. Formaggio, V. Setnicka, T. A. Keiderling, C. Toniolo, Journal of the 
American Chemical Society 126; 12874-12879 (2004). 

• Ab initio modeling of amide I coupling in anti -parallel b-sheets and the effect of the 13C isotopic labeling on 
vibrational spectra" Petr Bour, Timothy A. Keiderling, Journal of Physical Chemistry B, 109, 5348-5357 (2005) 

• Solvent Effects on IR And VCD Spectra of Helical Peptides: Insights from Ab Initio Spectral Simulations with 
Explicit Water" Jan Kubelka and Timothy A. Keiderling, Journal of Physical Chemistry B 109, 8231-8243 (2005) 

• IR Study of Cross-Strand Coupling in a beta-Hairpin Peptide Using Isotopic Labels., Vladimir Setnicka, Rong 
Huang, Catherine L. Thomas, Marcus A. Etienne, Jan Kubelka, Robert P. Hammer, Timothy A. Keiderling 
Journal of the American Chemical Society 127, 4992-4993 (2005). 

• Vibrational spectral simulation for peptides of mixed secondary structure: Method comparisons with the trpzip 
model hairpin. Petr Bour and Timothy A. Keiderling, Journal of Physical Chemistry B 109, 232687-23697 
(2005). 

• Isotopically labeled peptides provide site-resolved structural data with infrared spectra. Probing the structural 
limit of optical spectroscopy, Timothy A. Keiderling, Rong Huang, Jan Kubelka, Petr Bour, Vladimir Setnicka, 
Robert P. Hammer, Marcus *A. Etienne, R. A. Gangani D. Silva, Sean M. Decatur Collections Symposium 
Series, 8, 42-49 (2005) — ["Biologically Active Peptides" IXth Conference, Prague Czech Republic, April 20-22, 
2005. 



Vibrational circular dichroism 99 

Nucleic acids and polynucleotides 

• "Application of Vibrational Circular Dichroism to Synthetic Polypeptides and Polynucleic Acids" T. A. 
Keiderling, S. C. Yasui, R. K. Dukor, L. Yang, Polymer Preprints 30, 423-424 (1989). 

• "Vibrational Circular Dichroism of Polyribonucleic Acids. A Comparative Study in Aqueous Solution." A. 
Annamalai and T. A. Keiderling, Journal of the American Chemical Society, 109, 3125-3132 (1987). 

• "Conformational phase transitions (A-B and B-Z) of DNA and models using vibrational circular dichroism" L. 
Wang, L. Yang, T. A. Keiderling in Spectroscopy of Biological Molecules., eds. R. E. Hester, R. B. Girling, 
Special Publication 94 Roya 1 Society of Chemistry, Cambridge (1991) p. 137-38. 

• "Vibrational Circular Dichroism of Proteins Polysaccharides and Nucleic Acids" T. A. Keiderling, Chapter 8 in 
Physical Chemistry of Food Processes, Vol. 2 Advanced Techniques, Structures and Applications eds. I. C. 
Baianu, H. Pessen, T. Kumosinski, Van Norstrand — Reinhold, New York (1993) pp. 307—337. 

• "Structural Studies of Biological Macromolecules using Vibrational Circular Dichroism" T. A. Keiderling, P. 
Pancoska, Chapter 6 in Advances in Spectroscopy Vol. 21, "Biomolecular Spectroscopy Part B" ed. R. E. Hester, 
R. J. H. Clarke, John W iley Chichester (1993) pp 267-315. 

• "Detection of Triple Helical Nucleic Acids with Vibrational Circular Dichroism," L. Wang, P. Pancoska, T. A. 
Keiderling in "Fifth International Conference on The Spectroscopy of Biological Molecules" Th. Theophanides, J. 
Anastassopoulou, N. Fotopoul os (Eds), Kluwen Academic Publ., Dortrecht, 1993, p. 81-82. 

• "Helical Nature of Poly (dl-dC) ♦ Poly (dl-dC). Vibrational Circular Dichroism Results" L. Wang and T. A. 
Keiderling Nucleic Acids Research 21 4127-4132 (1993). 

• "Detection and Characterization of Triple Helical Pyrimidine-Purine-Pyrimidine Nucleic Acids with Vibrational 
Circular Dichroism" L. Wang, P. Pancoska, T. A. Keiderling, Biochemistry 33 8428-8435 (1994). 

• "Vibrational Circular Dichroism of A-, B- and Z- form Nucleic Acids in the P02- Stretching Region" L. Wang, L. 
Yang, T. A. Keiderling, Biophysical Journal 67, 2460-2467 (1994). 

• "Studies of multiple stranded RNA and DNA with FTIR, vibrational and electronic circular dichroism," Zhihua 
Huang, Lijiang Wang and Timothy A. Keiderling, in Spectrosopy of Biological Molecules, Ed. J. C. Merlin, 
Kluwer Acad. Pub., Dordrecht, 1995, pp . 321-322. 

• "Vibrational Circular Dichroism Applications to Conformational Analysis of Biomolecules" T. A. Keiderling in 
"Circular Dichroism and the Conformational Analysis of Biomolecules" ed G. D. Fasman, Plenum, New York 
(1996) pp. 555-598. 

• "Vibrational Circular Dichroism Techniques and Application to Nucleic Acids" T. A. Keiderling, In 
"Biomolecular Structure and Dynamics", NATO ASI series, Series E: Applied Sciences- Vol.342, Eds: G 
Vergoten and T. Theophanides, Kluwer Academ ic Publishers, Dordrecht, The Netherlands, pp. 299—317 (1997). 

See also 

Circular dichroism 

Birefringence 

Optical rotatory dispersion 

IR spectroscopy 

Polarization 

Proteins 

Nucleic Acids 

DNA 

Molecular models of DNA 

DNA structure 

Protein structure 

Amino acids 



Vibrational circular dichroism 100 

• Density functional theory 

• Quantum chemistry 

• Raman optical activity (ROA) 

References 

[I] http://planetphysics.org/?op=getobj;from=objects;id=410 Principles of IR and NIR Spectroscopy 

[2] *"Vibrational Circular Dichroism of Polypeptides XII. Re-evaluation of the Fourier Transform Vibrational Circular Dichroism of 

Poly-gamma-Benzyl-L-Glutamate," P. Malon, R. Kobrinskaya, T. A. Keiderling, Biopolymers 27, 733-746 (1988). 
[3] *"Vibrational Circular Dichroism of Biopolymers," T. A. Keiderling, S. C. Yasui, U. Narayanan, A. Annamalai, P. Malon, R. Kobrinskaya, 

L. Yang, in Spectroscopy of Biological Molecules New Advances ed. E. D. Schmid, F. W. Schneider, F. Siebert, p. 73-76 (1988). 
[4] *"Vibrational Circular Dichroism of Polypeptides and Proteins," S. C. Yasui, T. A. Keiderling, Mikrochimica Acta, II, 325-327, (1988). 
[5] *"Vibrational Circular Dichroism of Proteins Polysaccharides and Nucleic Acids" T. A. Keiderling, Chapter 8 in Physical Chemistry of Food 

Processes, Vol. 2 Advanced Techniques, Structures and Applications., eds. I.C. Baianu, H. Pessen, T. Kumosinski, Van Norstrand— Reinhold, 

New York (1993), pp 307-337. 
[6] "Spectroscopic characterization of Unfolded peptides and proteins studied with infrared absorption and vibrational circular dichroism spectra" 

T. A. Keiderling and Qi Xu, Advances in Protein Chemistry Volume 62, [Unfolded Proteins, Dedicated to John Edsall, Ed.: George Rose, 

Academic Press:New York] (2002), pp. 111-161. 
[7] *"Protein and Peptide Secondary Structure and Conformational Determination with Vibrational Circular Dichroism " Timothy A. Keiderling, 

Current Opinions in Chemical Biology (Ed. Julie Leary and Mark Arnold) 6, 682-688 (2002). 
[8] *Review: Conformational Studies of Peptides with Infrared Techniques. Timothy A. Keiderling and R. A. G. D. Silva, in Synthesis of 

Peptides and Peptidomimetics, Ed. M. Goodman and G. Herrman, Houben-Weyl, Vol 22Eb, Georg Thiem Verlag, New York (2002) pp. 

715-738, (written and accepted in 2000). 
[9] "Polarization Modulation Fourier Transform Infrared Spectroscopy with Digital SignalProcessing: Comparison of Vibrational Circular 

Dichroism Methods." Jovencio Hilario, DavidDrapcho, Raul Curbelo, Timothy A. Keiderling, Applied Spectroscopy 55, 1435-1447(2001)— 
[10] "Vibrational circular dichroism of biopolymers. Summary of methods and applications.", Timothy A. Keiderling, Jan Kubelka, Jovencio 

Hilario, in Vibrational spectroscopy of polymers and biological systems, Ed. Mark Braiman, Vasilis Gregoriou, Taylor&Francis, Atlanta 

(CRC Press, Boca Raton, FL) (2006) pp. 253-324 (originally written in 2000, updated in 2003) 

[II] "Observation of Magnetic Vibrational Circular Dichroism," T. A. Keiderling, Journal of Chemical Physics, 75, 3639-41 (1981). 

[12] "Vibrational Spectral Assignment and Enhanced Resolution Using Magnetic Vibrational Circular Dichroism," T. R. Devine and T. A. 

Keiderling, Spectrochimica Acta, 43A, 627-629 (1987). 
[13] "Magnetic Vibrational Circular Dichroism with an FTIR" P. V. Croatto, R. K. Yoo, T. A. Keiderling, SPIE Proceedings 1 145 (7th 

International Conference on FTS, ed. D. G. Cameron) 152-153 (1989). 
[14] "Direct Measurement of the Rotational g- Value in the Ground State of Acetylene by Magnetic Vibrational Circular Dichroism." C. N. Tarn 

and T. A. Keiderling, Chemical Physics Letters, 243, 55-58 (1995). 
[15] . "Ab initio calculation of the vibrational magnetic dipole moment" P. Bour, C. N. Tarn, T. A. Keiderling, Journal of Physical Chemistry 99, 

17810-17813 (1995) 
[16] "Rotationally Resolved Magnetic Vibrational Circular Dichroism. Experimental Spectra and Theoretical Simulation for Diamagnetic 

Molecules." P. Bour, C. N. Tarn, B. Wang, T. A. Keiderling, Molecular Physics 87, 299-318, (1996). 



Optical rotatory dispersion 



101 



Optical rotatory dispersion 



Optical rotatory dispersion is the variation in the optical rotation of a substance with a change in the wavelength of 
light. Optical rotatory dispersion can be used to find the absolute configuration of metal complexes. For example, 
when plane-polarized white light from an overhead projector is passed through a cylinder of sucrose solution, a 
spiral rainbow is observed perpendicular to the cylinder. 

When white light passes through a polarizer, the extent of rotation of light depends on its wavelength. Short 
wavelengths are rotated more than longer wavelengths. Because the wavelength of light determines its color, the 
variation of color with distance through the tube is observed. This dependence of specific rotation on wavelength is 
called optical rotatory dispersion. 



See also 

• Circular dichroism 



Raman spectroscopy 



Raman spectroscopy (named after C. 
V. Raman, pronounced /'ra:m9n/) is a 
spectroscopic technique used to study 
vibrational, rotational, and other 
low-frequency modes in a system. It 
relies on inelastic scattering, or Raman 
scattering, of monochromatic light, 
usually from a laser in the visible, near 
infrared, or near ultraviolet range. The 
laser light interacts with phonons or 
other excitations in the system, 
resulting in the energy of the laser 
photons being shifted up or down. The 
shift in energy gives information about 
the phonon modes in the system. 
Infrared spectroscopy yields similar, 
but complementary, information. 



Virtual 

energy 

states 



J 



Vibrational 
energy states 



± 



A 



I 



I 



I — 

Infrared Rayleigh Stokes Anti-Stokes 

absorption scattering Raman Raman 

scattering scattering 

Energy level diagram showing the states involved in Raman signal. The line thickness is 
roughly proportional to the signal strength from the different transitions. 



Typically, a sample is illuminated with 

a laser beam. Light from the illuminated spot is collected with a lens and sent through a monochromator. 
Wavelengths close to the laser line, due to elastic Rayleigh scattering, are filtered out while the rest of the collected 
light is dispersed onto a detector. 

Spontaneous Raman scattering is typically very weak, and as a result the main difficulty of Raman spectroscopy is 
separating the weak inelastically scattered light from the intense Rayleigh scattered laser light. Historically, Raman 
spectrometers used holographic gratings and multiple dispersion stages to achieve a high degree of laser rejection. In 
the past, photomultipliers were the detectors of choice for dispersive Raman setups, which resulted in long 
acquisition times. However, modern instrumentation almost universally employs notch or edge filters for laser 
rejection and spectrographs (either axial transmissive (AT), Czerny-Turner (CT) monochromator) or FT (Fourier 
transform spectroscopy based), and CCD detectors. 



Raman spectroscopy 102 

There are a number of advanced types of Raman spectroscopy, including surface-enhanced Raman, tip-enhanced 
Raman, polarised Raman, stimulated Raman (analogous to stimulated emission), transmission Raman, 
spatially-offset Raman, and hyper Raman. 

Basic theory 

The Raman effect occurs when light impinges upon a molecule and interacts with the electron cloud and the bonds of 
that molecule. For the spontaneous Raman effect, a photon excites the molecule from the ground state to a virtual 
energy state. When the molecule relaxes it emits a photon and it returns to a different rotational or vibrational state. 
The difference in energy between the original state and this new state leads to a shift in the emitted photon's 
frequency away from the excitation wavelength. 

If the final vibrational state of the molecule is more energetic than the initial state, then the emitted photon will be 
shifted to a lower frequency in order for the total energy of the system to remain balanced. This shift in frequency is 
designated as a Stokes shift. If the final vibrational state is less energetic than the initial state, then the emitted 
photon will be shifted to a higher frequency, and this is designated as an Anti-Stokes shift. Raman scattering is an 
example of inelastic scattering because of the energy transfer between the photons and the molecules during their 
interaction. 

A change in the molecular polarization potential — or amount of deformation of the electron cloud — with respect 
to the vibrational coordinate is required for a molecule to exhibit a Raman effect. The amount of the polarizability 
change will determine the Raman scattering intensity. The pattern of shifted frequencies is determined by the 
rotational and vibrational states of the sample. 

History 

Although the inelastic scattering of light was predicted by Adolf Smekal in 1923, it was not until 1928 that it was 
observed in practice. The Raman effect was named after one of its discoverers, the Indian scientist Sir C. V. Raman 
who observed the effect by means of sunlight (1928, together with K. S. Krishnan and independently by Grigory 
Landsberg and Leonid Mandelstam). Raman won the Nobel Prize in Physics in 1930 for this discovery 
accomplished using sunlight, a narrow band photographic filter to create monochromatic light and a "crossed" filter 
to block this monochromatic light. He found that light of changed frequency passed through the "crossed" filter. 

Systematic pioneering theory of the Raman effect was developed by Czechoslovak physicist George Placzek 

T21 
between 1930 and 1934. The mercury arc became the principal light source, first with photographic detection and 

then with spectrophotometric detection. Currently lasers are used as light sources. 

Applications 

Raman spectroscopy is commonly used in chemistry, since vibrational information is specific to the chemical bonds 
and symmetry of molecules. It therefore provides a fingerprint by which the molecule can be identified. For instance, 
the vibrational frequencies of SiO, Si O , and Si O were identified and assigned on the basis of normal coordinate 

2 2 3 3 

analyses using infrared and Raman spectra. The fingerprint region of organic molecules is in the (wavenumber) 
range 500—2000 cm - . Another way that the technique is used is to study changes in chemical bonding, e.g., when a 
substrate is added to an enzyme. 

Raman gas analyzers have many practical applications. For instance, they are used in medicine for real-time 
monitoring of anaesthetic and respiratory gas mixtures during surgery. 

In solid state physics, spontaneous Raman spectroscopy is used to, among other things, characterize materials, 
measure temperature, and find the crystallographic orientation of a sample. As with single molecules, a given solid 
material has characteristic phonon modes that can help an experimenter identify it. In addition, Raman spectroscopy 
can be used to observe other low frequency excitations of the solid, such as plasmons, magnons, and 



Raman spectroscopy 103 

superconducting gap excitations. The spontaneous Raman signal gives information on the population of a given 
phonon mode in the ratio between the Stokes (downshifted) intensity and anti-Stokes (upshifted) intensity. 

Raman scattering by an anisotropic crystal gives information on the crystal orientation. The polarization of the 
Raman scattered light with respect to the crystal and the polarization of the laser light can be used to find the 
orientation of the crystal, if the crystal structure (specifically, its point group) is known. 

Raman active fibers, such as aramid and carbon, have vibrational modes that show a shift in Raman frequency with 
applied stress. Polypropylene fibers also exhibit similar shifts. The radial breathing mode is a commonly used 
technique to evaluate the diameter of carbon nanotubes. In nanotechnology, a Raman microscope can be used to 
analyze nanowires to better understand the composition of the structures. 

Spatially-offset Raman spectroscopy (SORS), which is less sensitive to surface layers than conventional Raman, can 
be used to discover counterfeit drugs without opening their internal packaging, and for non-invasive monitoring of 

Ml 

biological tissue. Raman spectroscopy can be used to investigate the chemical composition of historical documents 



such as the Book of Kells and contribute to knowledge of the social and economic conditions at the time the 
documents were produced. This is especially helpful because Raman spectroscopy offers a non-invasive way to 
determine the best course of preservation or conservation treatment for such materials. 

Raman spectroscopy is being investigated as a means to detect explosives for airport security. 

Microspectroscopy 

Raman spectroscopy offers several advantages for microscopic analysis. Since it is a scattering technique, specimens 
do not need to be fixed or sectioned. Raman spectra can be collected from a very small volume (< 1 pm in diameter); 
these spectra allow the identification of species present in that volume. Water does not generally interfere with 
Raman spectral analysis. Thus, Raman spectroscopy is suitable for the microscopic examination of minerals, 
materials such as polymers and ceramics, cells and proteins. A Raman microscope begins with a standard optical 
microscope, and adds an excitation laser, a monochromator, and a sensitive detector (such as a charge-coupled 
device (CCD), or photomultiplier tube (PMT)). FT-Raman has also been used with microscopes. 

In direct imaging, the whole field of view is examined for scattering over a small range of wavenumbers (Raman 
shifts). For instance, a wavenumber characteristic for cholesterol could be used to record the distribution of 
cholesterol within a cell culture. 

The other approach is hyperspectral imaging or chemical imaging, in which thousands of Raman spectra are 
acquired from all over the field of view. The data can then be used to generate images showing the location and 
amount of different components. Taking the cell culture example, a hyperspectral image could show the distribution 
of cholesterol, as well as proteins, nucleic acids, and fatty acids. Sophisticated signal- and image-processing 
techniques can be used to ignore the presence of water, culture media, buffers, and other interferents. 

Raman microscopy, and in particular confocal microscopy, has very high spatial resolution. For example, the lateral 
and depth resolutions were 250 nm and 1.7 |am, respectively, using a confocal Raman microspectrometer with the 
632.8 nm line from a He-Ne laser with a pinhole of 100 |jm diameter. Since the objective lenses of microscopes 
focus the laser beam to several micrometres in diameter, the resulting photon flux is much higher than achieved in 
conventional Raman setups. This has the added benefit of enhanced fluorescence quenching. However, the high 
photon flux can also cause sample degradation, and for this reason some setups require a thermally conducting 
substrate (which acts as a heat sink) in order to mitigate this process. 

By using Raman microspectroscopy, in vivo time- and space-resolved Raman spectra of microscopic regions of 
samples can be measured. As a result, the fluorescence of water, media, and buffers can be removed. Consequently 
in vivo time- and space-resolved Raman spectroscopy is suitable to examine proteins, cells and organs. 

Raman microscopy for biological and medical specimens generally uses near-infrared (NIR) lasers (785 nm diodes 
and 1064 nm Nd:YAG are especially common). This reduces the risk of damaging the specimen by applying higher 



Raman spectroscopy 104 

4 

energy wavelengths. However, the intensity of NIR Raman is low (owing to the m dependence of Raman scattering 
intensity), and most detectors required very long collection times. Recently, more sensitive detectors have become 
available, making the technique better suited to general use. Raman microscopy of inorganic specimens, such as 
rocks and ceramics and polymers, can use a broader range of excitation wavelengths. 

Polarized analysis 

The polarization of the Raman scattered light also contains useful information. This property can be measured using 
(plane) polarized laser excitation and a polarization analyzer. Spectra acquired with the analyzer set at both 
perpendicular and parallel to the excitation plane can be used to calculate the depolarization ratio. Study of the 
technique is pedagogically useful in teaching the connections between group theory, symmetry, Raman activity and 
peaks in the corresponding Raman spectra. 

The spectral information arising from this analysis gives insight into molecular orientation and vibrational symmetry. 
In essence, it allows the user to obtain valuable information relating to the molecular shape, for example in synthetic 
chemistry or polymorph analysis. It is often used to understand macromolecular orientation in crystal lattices, liquid 

ro] 

crystals or polymer samples. 

Variations 

Several variations of Raman spectroscopy have been developed. The usual purpose is to enhance the sensitivity (e.g., 
surface-enhanced Raman), to improve the spatial resolution (Raman microscopy), or to acquire very specific 
information (resonance Raman). 

• Surface Enhanced Raman Spectroscopy (SERS) - Normally done in a silver or gold colloid or a substrate 
containing silver or gold. Surface plasmons of silver and gold are excited by the laser, resulting in an increase in 
the electric fields surrounding the metal. Given that Raman intensities are proportional to the electric field, there 
is large increase in the measured signal (by up to 10 ). This effect was originally observed by Martin 
Fleischmann but the prevailing explanation was proposed by Van Duyne in 1977. 

• Resonance Raman spectroscopy - The excitation wavelength is matched to an electronic transition of the 
molecule or crystal, so that vibrational modes associated with the excited electronic state are greatly enhanced. 
This is useful for studying large molecules such as polypeptides, which might show hundreds of bands in 
"conventional" Raman spectra. It is also useful for associating normal modes with their observed frequency 
shifts.™ 

• Surface Enhanced Resonance Raman Spectroscopy (SERRS) - A combination of SERS and resonance Raman 
spectroscopy which uses proximity to a surface to increase Raman intensity, and excitation wavelength matched 
to the maximum absorbance of the molecule being analysed. 

• Hyper Raman - A non-linear effect in which the vibrational modes interact with the second harmonic of the 
excitation beam. This requires very high power, but allows the observation of vibrational modes which are 
normally "silent". It frequently relies on SERS-type enhancement to boost the sensitivity. 

• Spontaneous Raman Spectroscopy - Used to study the temperature dependence of the Raman spectra of 
molecules. 

• Optical Tweezers Raman Spectroscopy (OTRS) - Used to study individual particles, and even biochemical 
processes in single cells trapped by optical tweezers. 

• Stimulated Raman Spectroscopy - A spatially coincedent, two color pulse (with polarization either parallel or 
perpendicular) transfers the population from ground to a rovibrationally excited state, if the difference in energy 
corresponds to an allowed Raman transition, and if neither frequency corresponds to an electronic resonance. Two 
photon UV ionization, applied after the population transfer but before relaxation, allows the intra-molecular or 
inter-molecular Raman spectrum of a gas or molecular cluster (indeed, a given conformation of molecular cluster) 
to be collected. This is a useful molecular dynamics technique. 



Raman spectroscopy 105 

• Spatially Offset Raman Spectroscopy (SORS) - The Raman scatter is collected from regions laterally offset 
away from the excitation laser spot, leading to significantly lower contributions from the surface layer than with 

ri2i 

traditional Raman spectroscopy. 

• Coherent anti-Stokes Raman spectroscopy (CARS) - Two laser beams are used to generate a coherent 
anti-Stokes frequency beam, which can be enhanced by resonance. 

• Raman optical activity (ROA) - Measures vibrational optical activity by means of a small difference in the 
intensity of Raman scattering from chiral molecules in right- and left-circularly polarized incident light or, 

ri3i 

equivalently, a small circularly polarized component in the scattered light. 

• Transmission Raman - Allows probing of a significant bulk of a turbid material, such as powders, capsules, 

ri4i 
living tissue, etc. It was largely ignored following investigations in the late 1960s but was rediscovered in 

2006 as a means of rapid assay of pharmaceutical dosage forms. There are also medical diagnostic 

applications. 

• Inverse Raman spectroscopy. 

• Tip-Enhanced Raman Spectroscopy (TERS) - Uses a metallic (usually silver-/gold-coated AFM or STM) tip to 
enhance the Raman signals of molecules situated in its vicinity. The spatial resolution is approximately the size of 
the tip apex (20-30 nm). TERS has been shown to have sensitivity down to the single molecule level. 

External links 

ri7i 

• An introduction to Raman spectroscopy , horiba.com 

n si 

• Raman Application examples , horiba.com 

• A introduction on Raman Scattering , d3technologies.co.uk 

• Raman Spectroscopy Applications , renishaw.com 

T211 

• Romanian Database of Raman Spectroscopy - This database contains mineral species (natural and synthetic) 

with description of crystal structure, sample image, number of sample, origin, Raman spectrum and vibrations, 
Raman discussion and references. Also, this site contains artefacts sample with sample image and pigment 
spectrum; black, red, white or blue pigment, rdrs.uaic.ro 

["221 

• Chemical Imaging Without Dyeing , witec.de 

• DoITPoMS Teaching and Learning Package - Raman Spectroscopy - an introduction, aimed at undergraduate 

level, doitpoms.ac.uk 

T241 

• Raman Spectroscopy Tutorial - A detailed explanation of Raman Spectroscopy including 

Resonance-Enhanced Raman Scattering and Surface-Enhanced Raman Scattering. 161.25.205.25 

• The Science Show, ABC Radio National - Interview with Scientist on NASA funded project to build Raman 
Spectrometer for the 2009 Mars mission: a cellular phone size device to detect almost any substance known, with 
commercial <USD$5000 commercial spin-off, prototyped by June 2006. abc.net.au/rn 

• Raman spectroscopy for medical diagnosis from the June 1, 2007 issue of Analytical Chemistry 
pubs.acs.org 

no] 

• Spontaneous Raman Scattering (SRS) , lavision.de 



Raman spectroscopy 106 

References 

[I] Gardiner, DJ. (1989). Practical Raman spectroscopy. Springer- Verlag. ISBN 978-0387502540. 

[2] Placzek G.: "Rayleigh Streeung und Raman Effekt", In: Hdb. der Radiologie, Vol. VI., 2, 1934, p. 209 

[3] Khanna, R.K. (1981). "Raman-spectroscopy of oligomeric SiO species isolated in solid methane". Journal of Chemical Physics. 

doi: 10.1063/1.441393. 
[4] . BBC News. 2007-01-31. http://news.bbc.co.Uk/2/hi/health/6314287.stm. Retrieved 2008-12-08. 
[5] Irish classic is still a hit (in calfskin, not paperback) - New York Times (http://www.nytimes.com/2007/05/28/world/europe/28kells. 

html), nytimes.com 
[6] Ben Vogel (29 August 2008). "Raman spectroscopy portends well for standoff explosives detection" (http://www.janes.com/news/ 

transport/business/jar/jar080829_l_n.shtml). Jane's. . Retrieved 2008-08-29. 
[7] Ellis DI, Goodacre R (August 2006). "Metabolic fingerprinting in disease diagnosis: biomedical applications of infrared and Raman 

spectroscopy". Analyst 131 (8): 875-85. doi:10.1039/b602376m. PMID 17028718. 
[8] Khanna, R.K. (1957). Evidence of ion-pairing in the polarized Raman spectra of a Ba2+CrO doped KI single crystal. John Wiley & Sons, 

Ltd. doi:10.1002/jrs.l250040104. 
[9] Jeanmaire DL, van Duyne RP (1977). "Surface Raman Electrochemistry Part I. Heterocyclic, Aromatic and Aliphatic Amines Adsorbed on 

the Anodized Silver Electrode". Journal of Electroanalytical Chemistry (Elsevier Sequouia S.A.) 84: 1—20. 

doi:10.1016/S0022-0728(77)80224-6. 
[10] Chao RS, Khanna RK, Lippincott ER (1974). "Theoretical and experimental resonance Raman intensities for the manganate ion". J Raman 

Spectroscopy 3: 121. doi:10.1002/jrs.l250030203. 

[II] Kneipp K, et al. (1999). "Surface-Enhanced Non-Linear Raman Scattering at the Single Molecule Level". Chem. Phys. 247: 155—162. 
doi:10.1016/S0301-0104(99)00165-2. 

[12] Matousek P, Clark IP, Draper ERC, et al. (2005). "Subsurface Probing in Diffusely Scattering Media using Spatially Offset Raman 

Spectroscopy". Applied Spectroscopy 59: 393. doi: 10. 1366/000370205775 142548. 
[13] Barron LD, Hecht L, McColl IH, Blanch EW (2004). "Raman optical activity comes of age". Molec. Phys. 102 (8): 73 1-744. 

doi: 10.1080/00268970410001704399. 
[14] B. Schrader, G. Bergmann, Fresenius. Z. (1967). Anal. Chem.: 225—230. 
[15] P. Matousek, A. W. Parker (2006). "Bulk Raman Analysis of Pharmaceutical Tablets". Applied Spectroscopy 60: 1353—1357. 

doi: 10.1366/000370206779321463. 
[16] P. Matousek, N. Stone (2007). "Prospects for the diagnosis of breast cancer by noninvasive probing of calcifications using transmission 

Raman spectroscopy". Journal of Biomedical Optics 12: 024008. doi: 10. 11 17/1.2718934. 
[17] http://www.horiba.com/us/en/scientific/products/raman-spectroscopy/raman-resource/raman-tutorial/ 
[18] http://www.horiba.com/scientific/products/raman-spectroscopy/application-notes/ 
[19] http://www.d3technologies.co.uk/en/10371.aspx 
[20] http://www.renishaw.com/en/raman-spectroscopy-applications--6259 
[21] http://rdrs.uaic.ro 

[22] http ://witec. de/en/download/Raman/ImagingMicroscopy04. pdf 
[23] http://www.doitpoms.ac.uk/tlplib/raman/index.php 
[24] http://161.58. 205. 25/Raman_Spectroscopy/rtr-ramantutorial.php?ss=800 
[25] http://www.abc.net.au/rn/science/ss/stories/sl581469.htm 

[26] http://pubs.acs.org/subscribe/journals/ancham/79/ill/pdf/0607feature_griffiths.pdf 
[27] http://pubs3.acs.org/acs/journals/toc.page?incoden=ancham&indecade=0&involume=79&inissue=ll 
[28] http://www.lavision.de/techniques/mie_raman_rayleigh/raman_imaging.php 



Coherent anti-Stokes Raman spectroscopy 



107 



Coherent anti-Stokes Raman spectroscopy 

Coherent anti-Stokes Raman spectroscopy, also called Coherent anti-Stokes Raman scattering spectroscopy 

(CARS), is a form of spectroscopy used primarily in chemistry, physics and related fields. It is sensitive to the same 

vibrational signatures of molecules as seen in Raman spectroscopy, typically the nuclear vibrations of chemical 

bonds. Unlike Raman spectroscopy, CARS employs multiple photons to address the molecular vibrations, and 

produces a signal in which the emitted waves are coherent with one another. As a result, CARS is orders of 

magnitude stronger than spontaneous Raman emission. CARS is a third-order nonlinear optical process involving 

three laser beams: a pump beam of frequency co , a Stokes beam of frequency co and a probe beam at frequency co . 

These beams interact with the sample and generate a coherent optical signal at the anti-Stokes frequency 

(co -co +co ). The latter is resonantly enhanced when the frequency difference between the pump and the Stokes 

beams (co -co ) coincides with the frequency of a Raman resonance, which is the basis of the technique's intrinsic 

P s in m 

vibrational contrast mechanism. 



History 

The acronym CARS, which invokes a seemingly inadvertent relation to automobiles, is actually closely related to the 
birth story of the technique. In 1965, a paper was published by two researchers of the Scientific Laboratory at the 
Ford Motor Company, P. D. Maker and R. W. Terhune, in which the CARS phenomenon was reported for the first 
time. Maker and Terhune used a pulsed ruby laser to investigate the third order response of several materials. They 
first passed the ruby beam of frequency co through a Raman shifter to create a second beam at co-co , and then 
directed the two beams simultaneously onto the sample. When the pulses from both beams overlapped in space and 
time, the Ford researchers observed a signal at co+co , which is the blue-shifted CARS signal. They also 
demonstrated that the signal increases significantly when the difference frequency co between the incident beams 
matches a Raman frequency of sample. Maker and Terhune called their technique simply 'three wave mixing 
experiments'. The name coherent anti-Stokes Raman spectroscopy was assigned almost ten years later, by Begley et 
al. at Stanford University in 1974. Since then, this vibrationally sensitive nonlinear optical technique is commonly 
known as CARS. 



Principle 

The CARS process can be physically explained by 

using either a classical oscillator model or by using a 

quantum mechanical model that incorporates the 

energy levels of the molecule. Classically, the Raman 

active vibrator is modeled as a (damped) harmonic 

oscillator with a characteristic frequency of co . In 

CARS, this oscillator is not driven by a single optical 

wave, but by the difference frequency (co -co ) between 

p s 

the pump and the Stokes beams instead. This driving 
mechanism is similar to hearing the low combination 
tone when striking two different high tone piano keys: 
your ear is sensitive to the difference frequency of the 
high tones. Similarly, the Raman oscillator is 
susceptible to the difference frequency of two optical 




Coherent anti-Stokes Raman spectroscopy 108 

waves. When the difference frequency to -co„ approaches to , the oscillator is driven very efficiently. On a molecular 
level, this implies that the electron cloud surrounding the chemical bond is vigorously oscillating with the frequency 
to -co . These electron motions alter the optical properties of the sample, i.e. there is a periodic modulation of the 
refractive index of the material. This periodic modulation can be probed by a third laser beam, the probe beam. 
When the probe beam is propagating through the periodically altered medium, it acquires the same modulation. Part 
of the probe, originally at to will now get modified to to +to -to„, which is the observed anti-Stokes emission. 

r ° J pr ° pr p S 

Under certain beam geometries, the anti-Stokes emission may diffract away from the probe beam, and can be 
detected in a separate direction. 

While intuitive, this classical picture does not take into account the quantum mechanical energy levels of the 
molecule. Quantum mechanically, the CARS process can be understood as follows. Our molecule is initially in the 
ground state, the lowest energy state of the molecule. The pump beam excites the molecule to a Virtual State. A 
virtual state is not an eigenstate of the molecule and it can not be occupied but it does allow for transitions between 
otherwise uncoupled real states. If a Stokes beam is simultaneously present along with the pump, the virtual state can 
be used as an instantaneous gateway to address a vibrational eigenstate of the molecule. The joint action of the pump 
and the Stokes has effectively established a coupling between the ground state and the vibrationally excited state of 
the molecule. The molecule is now in two states at the same time: it resides in a coherent superposition of states. 
This coherence between the states can be probed by the probe beam, which promotes the system to a virtual state. 
Again, the molecule cannot stay in the virtual state and will fall back instantaneously to the ground state under the 
emission of a photon at the anti-Stokes frequency. The molecule is no longer in a superposition, as it resides again in 
one state, the ground state. In the quantum mechanical model, no energy is deposited in the molecule during the 
CARS process. Instead, the molecule acts like a medium for converting the frequencies of the three incoming waves 
into a CARS signal (a parametric process). There are, however, related coherent Raman process that occur 
simultaneously which do deposit energy into the molecule. 

Comparison to Raman spectroscopy 

CARS is often compared to Raman spectroscopy as both techniques probe the same Raman active modes. Raman 
can be done using a single continuous wave (CW) laser whereas CARS requires (generally) two pulsed laser sources. 
The Raman signal is detected on the red side of the incoming radiation where it might have to compete with other 
fluorescent processes. The CARS signal is detected on the blue side, which is free from fluorescence, but it comes 
with a non-resonant contribution. The differences between the signals from Raman and CARS (there are many 
variants of both techniques) stems largely from the fact that Raman relies on a spontaneous transition whereas CARS 
relies on a coherently driven transition. The total Raman signal collected from a sample is the incoherent addition of 
the signal from individual molecules. It is therefore linear in the concentration of those molecules and the signal is 
emitted in all directions. The total CARS signal comes from a coherent addition of the signal from individual 
molecules. For the coherent addition to be additive, phase-matching must be fulfilled. For tight focusing conditions 
this is generally not a restriction. Once phase-matching is fulfilled the signal amplitude grows linear with distance so 
that the power grows quadratically. This signal forms a collimated beam that is therefore easily collected. The fact 
that the CARS signal is quadratic in the distance makes it quadratic with respect to the concentration and therefore 
especially sensitive to the majority constituent. The total CARS signal also contains an inherent non-resonant 
background. This non-resonant signal can be considered as the result of (several) far off-resonance transitions that 
also add coherently. The resonant amplitude contains a phase shift of Pi over the resonance whereas the non-resonant 
part does not. The spectral line shape of the CARS intensity therefore resembles a Fano-profile which is shifted with 
respect to the Raman signal. To compare the spectra from multi-component compounds, the (resonant) CARS 
spectral amplitude should be compared to the Raman spectral intensity. 

Theoretically Raman spectroscopy and CARS spectroscopy are equally sensitive as they use the same molecular 
transitions. However, given the limits on input power (damage threshold) and detector noise (integration time), the 



Coherent anti-Stokes Raman spectroscopy 109 

signal from a single transition can be collected much faster in practical situation (a factor of 10 ) using CARS. 
Imaging of known substances (known spectra) is therefore often done using CARS. Given the fact that CARS is a 
higher order nonlinear process, the CARS signal from a single molecule is larger than the Raman signal from a 
single molecule for a sufficiently high driving intensity. However at very low concentrations, the advantages of the 
coherent addition for CARS signal reduces and the presence of the incoherent background becomes an increasing 
problem. 

Since CARS is such a nonlinear process there are not really any 'typical' experimental numbers. One example is 
given below under the explicit warning that just changing the pulse duration by one order of magnitude changes the 
CARS signal by three orders of magnitude. The comparison should only be used as an indication of the order of 
magnitude of the signals. 200 mW average power input (CW for the Raman), in a 0.9NA objective with a center 

2 

wavelength around 800 nm, constitutes a power density of 26 MW/cm, (focal length =1.5 micrometre, focal 

3 -19 

volume =1.16 micrometre , photon energy = 2.31 10 J or 1.44 eV). The Raman cross section for the vibration of 

-1 -29 2 

the aromatic ring in Toluene around 1000 cm is on the order of 10 cm /molecule*steradian. Therefore the Raman 

-22 -21 

signal is around 26 10 W/molecule*steradian or 3.3 10 W/molecule (over 4Pi). That is 0.014 

3 3 -3 

photon/sec*molecule. The density of Toluene = 0.8668 10 kg/m , Molecular mass = 92.14 10 kg/mol. Therefore 

9 
the focal volume (~1 cubic micrometre) contains 6 10 molecules. Those molecules together generate a Raman 

signal in the order of 2 10 W (20pW) or roughly one hundred million photons/sec (over a 4Pi solid angle). A 

CARS experiment with similar parameters (150 mW at 1064 nm, 200 mW at 803.5 nm, 15ps pulses at 80Mhz 

repetition frequency, same objective lens) yields roughly 17.5 10" W (on the 3000 cm" line, which has 1/3 of the 

strength and roughly 3 times the width). This CARS power is roughly 10 higher than the Raman but since there are 

6 10 molecules, the signal per molecule from CARS is only 4 10 W/molecule*sec or 1.7 10 

photons/molecule*sec. If we allow for two factors of three (line strength and line width) than the spontaneous 

Raman signal per molecule still exceeds the CARS per molecule by a more than two orders of magnitude. The 

coherent addition of the CARS signal from the molecules however yields a total signal that is much higher than the 

Raman. 

The sensitivity in many CARS experiments is not limited by the detection of CARS photons but rather by the 
distinction between the resonant and non-resonant part of the CARS signal. 

Applications 

CARS is used for species selective microscopy and combustion diagnostics. The first exploits the selectivity of 
vibrational spectroscopy whereas the latter is aimed at temperature measurements; the CARS signal is temperature 
dependent. The strength of the signal scales (non-linearly) with the difference in the ground state population and the 
vibrationally excited state population. Since the population of states follows the temperature dependent Boltzmann 
Distribution, the CARS signal carries an intrinsic temperature dependence as well. This temperature dependence 
makes CARS a popular technique for monitoring the temperature of hot gases and flames. 



Coherent anti-Stokes Raman spectroscopy 



110 



See also 

• Coherent Stokes Raman spectroscopy 

• Raman spectroscopy 

• Four-wave mixing 

References 

[1] A Review of the Theory and Application of Coherent Anti-Stokes Raman Spectroscopy (CARS) Applied Spectroscopy, Volume 31, Number 

4, July/August 1977, pp. 253-271(19) (http://www.ingentaconnect.com/content/sas/sas/1977/00000031/00000004/art00001) 
[2] Coherent anti-Stokes Raman scattering: from proof-of-the-principle experiments to femtosecond CARS and higher order wave-mixing 

generalizations Journal of Raman Spectroscopy, Volume 31, Issue 8-9 , pp. 653 - 667 (http://www3.interscience.wiley.com/cgi-bin/ 

abstract/73500427/ABSTRACT?CRETRY=l&SRETRY=0) 
[3] Study of Optical Effects Due to an Induced Polarization Third Order in the Electric Field Strength Physical Review, Volume 137, Issue 3A, 

pp. 801-818 (http://prola.aps.org/abstract/PR/vl37/i3A/pA801_l) 
[4] Coherent anti-Stokes Raman spectroscopy Applied Physics Letters, Volume 25, Issue 7 , pp. 387-390 (http://scitation.aip.org/getabs/ 

servlet/GetabsServlet?prog=normal&id=APPLAB000025000007000387000001&idtype=cvips&gifs=yes) 



Raman Microscopy 



Raman microscope begins with a standard optical microscope, and adds an excitation laser, a monochromator, and 
a optical sensitive detector such as a charge-coupled device (CCD), or photomultiplier tube, (PMT)), and has been 
implemented for Raman spectroscopy in direct chemical imaging, the whole field of view on 3D sample. 



Imaging spectroscopy 



Imaging spectroscopy (also spectral imaging, 

chemical imaging, or microspectroscopy) is similar to 
color photography, but each pixel acquires many bands 
of light intensity data from the spectrum, instead of just 
the three bands of the RGB color model. More 
precisely, it is the simultaneous acquisition of spatially 
coregistered images in many spectrally contiguous 
bands. 




Ash plumes on Kamchatka Peninsula, eastern Russia. A MODIS 
image. 



Some spectral images contain only a few image planes of spectral data, while others are better thought of as full 
spectra at every location in the image. For example, solar physicists use the spectroheliograph, to make images of the 
Sun built up by scanning the slit of a spectrograph, to study the behavior of surface features on the Sun; such a 
spectroheliogram may have a spectral resolution of over 100,000 ( A/AA ) and be used to measure local motion 
(via the Doppler shift) and even the magnetic field (via the Zeeman splitting or Hanle effect) at each location in the 
image plane. The multispectral images collected by the Opportunity rover, in contrast, have only four wavelength 



Imaging spectroscopy 111 

bands and hence are only a little more than 3-color images. 

To be scientifically useful, such measurement should be done using an internationally recognized system of units. 

One example application is geophysical spectral imaging, which allows quantitative and qualitative characterization 
of both, the surface and the atmosphere, using geometrically coherent spectrodirectional radiometric measurements. 
These measurements can then be used for the unambiguous direct and indirect identification of surface materials and 
atmospheric trace gases, the measurement of their relative concentrations, subsequently the assignment of the 
proportional contribution of mixed pixel signals (e.g., the spectral unmixing problem), the derivation of their spatial 
distribution (mapping problem), and finally their study over time (multi-temporal analysis). The Moon Mineralogy 
Mapper on Chandrayaan-1 was an imaging spectrometer. 

Background 

About 300 years ago, in 1704, Sir Isaac Newton published in his 'Treatise of Light' (Newton, 1704) the concept of 
dispersion of light. He demonstrated that white light could be split up into component colours by means of a prism, 
and found that each pure colour is characterized by a specific refrangibility. The corpuscular theory by Newton was 
gradually succeeded over time by the wave theory. Consequently, the substantial summary of past experiences 
performed by Maxwell (1873), resulted in his equations of electromagnetic waves. But it was not until the 19th 
century that the quantitative measurement of dispersed light was recognized and standardized. 

A major contribution was Fraunhofer's discovery of the dark lines in the solar spectrum (Fraunhofer, 1817); and their 
interpretation as absorption lines on the basis of experiments by Bunsen and Kirchhoff (1863). The term 
"spectroscopy" was first used in the late 19th century and provides the empirical foundations for atomic and 
molecular physics (Born & Wolf, 1999). Significant achievements in imaging spectroscopy are attributed to airborne 
instruments, particularly arising in the early 1980s and 1990s (Goetz et al., 1985; Vane et al., 1984). However, it was 
not until 1999 that the first imaging spectrometer was launched in space (the NASA Moderate-resolution Imaging 
Spectroradiometer, or MODIS). 

Terminology and definitions evolve over time. At one time, >10 spectral bands sufficed to justify the term "imaging 
spectrometer" but presently the term is seldom defined by a total minimum number of spectral bands, rather by a 
contiguous (or redundant) statement of spectral bands. 

The term hyperspectral imaging is sometimes used interchangeably with imaging spectroscopy. Due to its heavy use 
in military related applications, the civil world has established a slight preference for using the term imaging 
spectroscopy. 

Unmixing 

Hyperspectral data is often used to determine what materials are present in a scene. Materials of interest could 
include roadways, vegetation, and specific targets (i.e. pollutants, hazardous materials, etc). Trivially, each pixel of a 
hyperpsectral image could be compared to a material database to determine the type of material making up the pixel. 
However, many hyperspectral imaging platforms have low resolution (>5m per pixel) causing each pixel to be a 
mixture of several materials. The process of unmixing one of these 'mixed' pixels is called hyperspectral image 
unmixing or simply hyperspectral unmixing. 

Models 

A solution to hyperspectral unmixing is to reverse the mixing process. Generally, two models of mixing are 
assumed: linear and nonlinear. Linear mixing models the ground as being flat and incident sunlight on the ground 
causes the materials to radiate some amount of the incident energy back to the sensor. Each pixel then, is modeled as 
a linear sum of all the radiated energy curves of materials making up the pixel. Therefore, each material contributes 
to the sensor's observation in a positive linear fashion. Additionally, a conservation of energy constraint is often 



Imaging spectroscopy 112 

observed thereby forcing the weights of the linear mixture to sum to one in addition to being positive. The model can 
be described mathematically as follows: 

p = A * X 
where p represents a pixel observed by the sensor, J\_ is a matrix of material reflectance signatures (each signature 
is a column of the matrix), and x is the proportion of material present in the observed pixel. This type of model is 
also referred to as a simplex. 

With x satisfying the two constraints: 1. Abundance Nonnegativty Constraint (ANC) - each element of x is positive. 
2. Abundance Sum-to-one Constraint (ASC) - the elements of x must sum to one. 

Non-linear mixing results from multiple scattering often due to non-flat surface such as buildings and vegetation. 

Unmixing (Endmember Detection) Algorithms 

There are many algorithms to unmix hyperspectral data each with their own strengths and weaknesses. Many 
algorithms assume that pure pixels (pixels which contain only one materials) are present in a scene. Some algorithms 
to perform unmixing are listed below: 

• Pixel Purity Index (PPI) - Works by projecting each pixel onto one vector from a set of random vectors spanning 
the reflectance space. A pixel receives a score when it represent an extremum of all the projections. Pixels with 
the highest scores are deemed to be spectrally pure. 

• NFINDR 

• Gift Wrapping Algorithm 

• Independent Component Analysis Endmember Extraction Algorithm (ICA-EEA) - Works by assuming that pure 
pixels occur independently than mixed pixels. Assumes pure pixels are present. 

• Vertex Component Analysis (VCA) - Works on the fact that the affine transformation of a simplex is another 
simplex which helps to find hidden (folded) verticies of the simplex. Assumes pure pixels are present. 

• Principal component analysis -(PCA) could also be used to determine endmembers, projection on principal axes 
could permit endmember selection [ Smith, Johnson et Adams (1985), Bateson et Curtiss (1996) ] 

• Multi Endmembers Spatial Mixture Analysis (MESMA) based on the SMA algorithm 

Non-linear unmixing algortithm also exist (Support Vector Machines (SVM)) or Analytical Neural Network (ANN). 
Probabilistics methods have also been attempted to unmix pixel through Monte Carlo Unmixing (MCU) algorithm. 

Abundance Maps 

Once the fundamental materials of a scene are determined, it is often useful to construct an abundance map of each 
material which displays the fractional amount of material present at each pixel. Often linear programming is done to 
observed ANC and ASC. 

Sensors 

AVIRIS — aircraft, (224 bands) 

Telops Hyper-Cam — Commercial infrared hyperspectral camera, ground-based or aircraft 

MODIS — on board EOS Terra and Aqua platforms 

MERIS — on board Envisat 

HyDice 

Hyperion — on board the Earth Observing 1 satellite 



Imaging spectroscopy 113 

See also 

Remote sensing 

Hyperspectral 

Full Spectral Imaging 

List of Earth observation satellites 

Chemical Imaging 

Imaging spectrometer 

Infrared Microscopy 

References 

[1] Large quantities of water found on the Moon (http://www.telegraph.co.uk/science/space/6224974/ 

Large-quantities-of-water-found-on-the-Moon.html) 
[2] http://www.hyper-cam.com/ 

• Born, M. & Wolf, E. (1999) Principles of Optics, 7 edn. Cambridge University Press, Cambridge. 

• Bunsen, R. & Kirchhoff, G. (1863) Untersuchungen iiber das Sonnenspektrum und die Spektren der Chemischen 
Elemente. Abh. kgl. Akad. Wiss., 1861. 

• Fraunhofer, J. (1817) Bestimmung des Brechungs- und Farbenzerstreuungs-Vermogens verschiedener Glasarten, 
in Bezug auf die Vervollkommnung achromatischer Fernrohre, Vol. 56, pp. 264—313. Gilberts Annalen der 
Physik. 

• Goetz, A.F.H., Vane, G, Solomon, J.E., & Rock, B.N. (1985) Imaging spectrometry for earth remote sensing. 
Science, 228, 1147. 

• Maxwell, J.C. (1873) A Treatise on Electricity and Magnetism Clarendon Press, Oxford. 

• Newton, I. (1704) Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light Sam 
Smith and Benj. Walford, London. 

• Schaepman, M. (2005) Spectrodirectional Imaging: From Pixels to Processes. Inaugural address, Wageningen 
University, Wageningen (NL). 

• Vane, G., Chrisp, M., Emmark, H., Macenka, S., & Solomon, J. (1984) Airborne Visible Infrared Imaging 
Spec-trometer (AVIRIS): An Advanced Tool for Earth Remote Sensing. European Space Agency, (Special 
Publication) ESA SP, 2, 751. 

External links 

• About imaging spectroscopy (USGS): http://speclab.cr.usgs.gov/aboutimsp.html 

• Link to resources (OKSI): http://www.techexpo.com/WWW/opto-knowledge/IS_resources.html 

• Special Interest Group Imaging Spectroscopy (EARSeL): http://www.op.dlr.de/dais/SIGTS/SIG-IS.html 

• Applications of Spectroscopic and Chemical Imaging in Research: http://www3.imperial.ac.uk/ 
vibrationalspectroscopyandchemicalimaging/research 



Chemical imaging 114 



Chemical imaging 



Chemical imaging is the analytical capability (as quantitative - mapping) to create a visual image from simultaneous 
measurement of spectra (as quantitative - chemical) and spatial, time informations. The technique is most often 

applied to either solid or gel samples, and has applications in chemistry, biology , medicine 

rm r22i ri2i r i3i 

pharmacy (see also for example: Chemical Imaging Without Dyeing ), food science, biotechnology 

ri4i 

agriculture and industry (see for example:NIR Chemical Imaging in Pharmaceutical Industry and Pharmaceutical 
Process Analytical Technology: ). NIR, IR and Raman chemical imaging is also referred to as hyperspectral, 
spectroscopic, spectral or multispectral imaging (also see microspectroscopy). However, other ultra-sensitive and 
selective, chemical imaging techniques are also in use that involve either UV-visible or fluorescence 
microspectroscopy. Chemical imaging techniques can be used to analyze samples of all sizes, from the single 
molecule to the cellular level in biology and medicine , and to images of planetary systems in 

astronomy, but different instrumentation is employed for making observations on such widely different systems. 

Chemical imaging instrumentation is composed of three components: a radiation source to illuminate the sample, a 
spectrally selective element, and usually a detector array (the camera) to collect the images. When many stacked 
spectral channels (wavelengths) are collected for different locations of the microspectrometer focus on a line or 
planar array in the focal plane, the data is called hyperspectral; fewer wavelength data sets are called multispectral. 
The data format is called a hypercube. The data set may be visualized as a three-dimensional block of data spanning 
two spatial dimensions (x and y), with a series of wavelengths (lambda) making up the third (spectral) axis. The 
hypercube can be visually and mathematically treated as a series of spectrally resolved images (each image plane 
corresponding to the image at one wavelength) or a series of spatially resolved spectra. The analyst may choose to 
view the spectrum measured at a particular spatial location; this is useful for chemical identification. Alternatively, 
selecting an image plane at a particular wavelength can highlight the spatial distribution of sample components, 
provided that their spectral signatures are different at the selected wavelength. 

Many materials, both manufactured and naturally occurring, derive their functionality from the spatial distribution of 
sample components. For example, extended release pharmaceutical formulations can be achieved by using a coating 
that acts as a barrier layer. The release of active ingredient is controlled by the presence of this barrier, and 
imperfections in the coating, such as discontinuities, may result in altered performance. In the semi-conductor 
industry, irregularities or contaminants in silicon wafers or printed micro-circuits can lead to failure of these 
components. The functionality of biological systems is also dependent upon chemical gradients — a single cell, 
tissue, and even whole organs function because of the very specific arrangement of components. It has been shown 
that even small changes in chemical composition and distribution may be an early indicator of disease. 

Any material that depends on chemical gradients for functionality may be amenable to study by an analytical 
technique that couples spatial and chemical characterization. To efficiently and effectively design and manufacture 
such materials, the 'what' and the 'where' must both be measured. The demand for this type of analysis is increasing 
as manufactured materials become more complex. Chemical imaging techniques not only permit visualization of the 
spatially resolved chemical information that is critical to understanding modern manufactured products, but it is also 
a non-destructive technique so that samples are preserved for further testing. 

History 

Commercially available laboratory-based chemical imaging systems emerged in the early 1990s (ref. 1-5). In 
addition to economic factors, such as the need for sophisticated electronics and extremely high-end computers, a 
significant barrier to commercialization of infrared imaging was that the focal plane array (FPA) needed to read IR 
images were not readily available as commercial items. As high-speed electronics and sophisticated computers 
became more commonplace, and infrared cameras became readily commercially available, laboratory chemical 
imaging systems were introduced. 



Chemical imaging 115 

Initially used for novel research in specialized laboratories, chemical imaging became a more commonplace 
analytical technique used for general R&D, quality assurance (QA) and quality control (QC) in less than a decade. 
The rapid acceptance of the technology in a variety of industries (pharmaceutical, polymers, semiconductors, 
security, forensics and agriculture) rests in the wealth of information characterizing both chemical composition and 
morphology. The parallel nature of chemical imaging data makes it possible to analyze multiple samples 
simultaneously for applications that require high throughput analysis in addition to characterizing a single sample. 

Principles 

Chemical imaging shares the fundamentals of vibrational spectroscopic techniques, but provides additional 
information by way of the simultaneous acquisition of spatially resolved spectra. It combines the advantages of 
digital imaging with the attributes of spectroscopic measurements. Briefly, vibrational spectroscopy measures the 
interaction of light with matter. Photons that interact with a sample are either absorbed or scattered; photons of 
specific energy are absorbed, and the pattern of absorption provides information, or a fingerprint, on the molecules 
that are present in the sample. 

On the other hand, in terms of the observation setup, chemical imaging can be carried out in one of the following 
modes: (optical) absorption, emission (fluorescence), (optical) transmission or scattering (Raman). A consensus 
currently exists that the fluorescence (emission) and Raman scattering modes are the most sensitive and powerful, 
but also the most expensive. 

In a transmission measurement, the radiation goes through a sample and is measured by a detector placed on the far 
side of the sample. The energy transferred from the incoming radiation to the molecule(s) can be calculated as the 
difference between the quantity of photons that were emitted by the source and the quantity that is measured by the 
detector. In a diffuse reflectance measurement, the same energy difference measurement is made, but the source and 
detector are located on the same side of the sample, and the photons that are measured have re-emerged from the 
illuminated side of the sample rather than passed through it. The energy may be measured at one or multiple 
wavelengths; when a series of measurements are made, the response curve is called a spectrum. 

A key element in acquiring spectra is that the radiation must somehow be energy selected — either before or after 
interacting with the sample. Wavelength selection can be accomplished with a fixed filter, tunable filter, 
spectrograph, an interferometer, or other devices. For a fixed filter approach, it is not efficient to collect a significant 
number of wavelengths, and multispectral data are usually collected. Interferometer-based chemical imaging requires 
that entire spectral ranges be collected, and therefore results in hyperspectral data. Tunable filters have the flexibility 
to provide either multi- or hyperspectral data, depending on analytical requirements. 

Spectra may be measured one point at a time using a single element detector (single-point mapping), as a line-image 
using a linear array detector (typically 16 to 28 pixels) (linear array mapping), or as a two-dimensional image using a 
Focal Plane Array (FPA)(typically 256 to 16,384 pixels) (FPA imaging). For single-point the sample is moved in the 
x and y directions point-by-point using a computer-controlled stage. With linear array mapping, the sample is moved 
line-by-line with a computer-controlled stage. FPA imaging data are collected with a two-dimensional FPA detector, 
hence capturing the full desired field-of-view at one time for each individual wavelength, without having to move 
the sample. FPA imaging, with its ability to collected tens of thousands of spectra simultaneously is orders of 
magnitude faster than linear arrays which are can typically collect 16 to 28 spectra simultaneously, which are in turn 
much faster than single-point mapping. 



Chemical imaging 



116 



Terminology 

Some words common in spectroscopy, optical microscopy and photography have been adapted or their scope 
modified for their use in chemical imaging. They include: resolution, field of view and magnification. There are two 
types of resolution in chemical imaging. The spectral resolution refers to the ability to resolve small energy 
differences; it applies to the spectral axis. The spatial resolution is the minimum distance between two objects that is 
required for them to be detected as distinct objects. The spatial resolution is influenced by the field of view, a 
physical measure of the size of the area probed by the analysis. In imaging, the field of view is a product of the 
magnification and the number of pixels in the detector array. The magnification is a ratio of the physical area of the 
detector array divided by the area of the sample field of view. Higher magnifications for the same detector image a 
smaller area of the sample. 

Types of vibrational chemical imaging instruments 

Chemical imaging has been implemented for mid-infrared, near-infrared spectroscopy and Raman spectroscopy. As 
with their bulk spectroscopy counterparts, each imaging technique has particular strengths and weaknesses, and are 
best suited to fulfill different needs. 



Mid-infrared chemical imaging 

Mid-infrared (MIR) spectroscopy probes fundamental molecular vibrations, which arise in the spectral range 
2,500-25,000 nm. Commercial imaging implementations in the MIR region typically employ Fourier Transform 
Infrared (FT-IR) interferometers and the range is more commonly presented in wavenumber, 4,000 — 400 cm" . The 
MIR absorption bands tend to be relatively narrow and well-resolved; direct spectral interpretation is often possible 
by an experienced spectroscopist. MIR spectroscopy can distinguish subtle changes in chemistry and structure, and is 
often used for the identification of unknown materials. The absorptions in this spectral range are relatively strong; 
for this reason, sample presentation is important to limit the amount of material interacting with the incoming 
radiation in the MIR region. Most data collected in this range is collected in transmission mode through thin sections 
(-10 micrometres) of material. Water is a very strong absorber of MIR radiation and wet samples often require 
advanced sampling procedures (such as attenuated total reflectance). Commercial instruments include point and line 
mapping, and imaging. All employ an FT-IR interferometer as wavelength selective element and light source. 

For types of MIR microscope, see 
Microscopy#Infrared microscopy. 

Atmospheric windows in the infrared 

spectrum are also employed to perform 

chemical imaging remotely. In these spectral 

regions the atmospheric gases (mainly water 

and CO ) present low absorption and allow 

infrared viewing over kilometer distances. 

Target molecules can then be viewed using 

the selective absorption/emission processes 

described above. An example of the chemical imaging of a simultaneous release of SF and NH is shown in the 

image. 




Remote chemical imaging of a simultaneous release of SF and NH at 1 .5km using 

V&\ 3 

the FIRST imaging spectrometer 



Chemical imaging 117 

Near-infrared chemical imaging 

The analytical near infrared (NIR) region spans the range from approximately 700-2,500 nm. The absorption bands 
seen in this spectral range arise from overtones and combination bands of O-H, N-H, C-H and S-H stretching and 
bending vibrations. Absorption is one to two orders of magnitude smaller in the NIR compared to the MIR; this 
phenomenon eliminates the need for extensive sample preparation. Thick and thin samples can be analyzed without 
any sample preparation, it is possible to acquire NIR chemical images through some packaging materials, and the 
technique can be used to examine hydrated samples, within limits. Intact samples can be imaged in transmittance or 
diffuse reflectance. 

The lineshapes for overtone and combination bands tend to be much broader and more overlapped than for the 
fundamental bands seen in the MIR. Often, multivariate methods are used to separate spectral signatures of sample 
components. NIR chemical imaging is particularly useful for performing rapid, reproducible and non-destructive 

[22] [231 

analyses of known materials . NIR imaging instruments are typically based on one of two platforms: imaging 

using a tunable filter and broad band illumination, and line mapping employing an FT-IR interferometer as the 
wavelength filter and light source. 

Raman chemical imaging 

The Raman shift chemical imaging spectral range spans from approximately 50 to 4,000 cm" ; the actual spectral 
range over which a particular Raman measurement is made is a function of the laser excitation frequency. The basic 
principle behind Raman spectroscopy differs from the MIR and NIR in that the x-axis of the Raman spectrum is 
measured as a function of energy shift (in cm" ) relative to the frequency of the laser used as the source of radiation. 
Briefly, the Raman spectrum arises from inelastic scattering of incident photons, which requires a change in 
polarizability with vibration, as opposed to infrared absorption, which requires a change in dipole moment with 
vibration. The end result is spectral information that is similar and in many cases complementary to the MIR. The 

7 

Raman effect is weak - only about one in 10 photons incident to the sample undergoes Raman scattering. Both 
organic and inorganic materials possess a Raman spectrum; they generally produce sharp bands that are chemically 
specific. Fluorescence is a competing phenomenon and, depending on the sample, can overwhelm the Raman signal, 
for both bulk spectroscopy and imaging implementations. 

Raman chemical imaging requires little or no sample preparation. However, physical sample sectioning may be used 
to expose the surface of interest, with care taken to obtain a surface that is as flat as possible. The conditions required 
for a particular measurement dictate the level of invasiveness of the technique, and samples that are sensitive to high 
power laser radiation may be damaged during analysis. It is relatively insensitive to the presence of water in the 
sample and is therefore useful for imaging samples that contain water such as biological material. 

Fluorescence imaging (visible and NIR) 

This emission microspectroscopy mode is the most sensitive in both visible and FT-NIR microspectroscopy, and has 
therefore numerous biomedical, biotechnological and agricultural applications. There are several powerful, highly 
specific and sensitive fluorescence techniques that are currently in use, or still being developed; among the former 
are FLIM, FRAP, FRET and FLIM-FRET; among the latter are NIR fluorescence and probe-sensitivity enhanced 
NIR fluorescence microspectroscopy and nanospectroscopy techniques (see "Further reading" section). 

Sampling and samples 

The value of imaging lies in the ability to resolve spatial heterogeneities in solid-state or gel/gel-like samples. 
Imaging a liquid or even a suspension has limited use as constant sample motion serves to average spatial 
information, unless ultra-fast recording techniques are employed as in fluorescence correlation microspectroscopy or 
FLIM obsevations where a single molecule may be monitored at extremely high (photon) detection speed. 
High-throughput experiments (such as imaging multi-well plates) of liquid samples can however provide valuable 



Chemical imaging 118 

information. In this case, the parallel acquisition of thousands of spectra can be used to compare differences between 
samples, rather than the more common implementation of exploring spatial heterogeneity within a single sample. 

Similarly, there is no benefit in imaging a truly homogeneous sample, as a single point spectrometer will generate 
the same spectral information. Of course the definition of homogeneity is dependent on the spatial resolution of the 
imaging system employed. For MIR imaging, where wavelengths span from 3-10 micrometres, objects on the order 
of 5 micrometres may theoretically be resolved. The sampled areas are limited by current experimental 
implementations because illumination is provided by the interferometer. Raman imaging may be able to resolve 
particles less than 1 micrometre in size, but the sample area that can be illuminated is severely limited. With Raman 
imaging, it is considered impractical to image large areas and, consequently, large samples. FT-NIR 
chemical/hyperspectral imaging usually resolves only larger objects (>10 micrometres), and is better suited for large 

samples because illumination sources are readily available. However, FT-NIR microspectroscopy was recently 

T241 
reported to be capable of about 1.2 micron (micrometer) resolution in biological samples Furthermore, 

two-photon excitation FCS experiments were reported to have attained 15 nanometer resolution on biomembrane 

thin films with a special coincidence photon-counting setup. 

Detection limit 

The concept of the detection limit for chemical imaging is quite different than for bulk spectroscopy, as it depends 
on the sample itself. Because a bulk spectrum represents an average of the materials present, the spectral signatures 
of trace components are simply overwhelmed by dilution. In imaging however, each pixel has a corresponding 
spectrum. If the physical size of the trace contaminant is on the order of the pixel size imaged on the sample, its 
spectral signature will likely be detectable. If however, the trace component is dispersed homogeneously (relative to 
pixel image size) throughout a sample, it will not be detectable. Therefore, detection limits of chemical imaging 
techniques are strongly influenced by particle size, the chemical and spatial heterogeneity of the sample, and the 
spatial resolution of the image. 

Data analysis 

Data analysis methods for chemical imaging data sets typically employ mathematical algorithms common to single 
point spectroscopy or to image analysis. The reasoning is that the spectrum acquired by each detector is equivalent to 
a single point spectrum; therefore pre-processing, chemometrics and pattern recognition techniques are utilized with 
the similar goal to separate chemical and physical effects and perform a qualitative or quantitative characterization of 
individual sample components. In the spatial dimension, each chemical image is equivalent to a digital image and 
standard image analysis and robust statistical analysis can be used for feature extraction. 

See also 

• Multispectral image 

• Microspectroscopy 

• Imaging spectroscopy 

Further reading 

1. E. N. Lewis, P. J. Treado, I. W. Levin, Near-Infrared and Raman Spectroscopic Imaging, American Laboratory, 
06/1994:16(1994) 

2. E. N. Lewis, P. J. Treado, R. C. Reeder, G. M. Story, A. E. Dowrey, C. Marcott, I. W. Levin, FTIR spectroscopic 
imaging using an infrared focal-plane array detector, Analytical Chemistry, 67:3377 (1995) 

3. P. Colarusso, L. H. Kidder, I. W. Levin, J. C. Fraser, E. N. Lewis Infrared Spectroscopic Imaging: from Planetary 
to Cellular Systems, Applied Spectroscopy, 52 (3):106A (1998) 



Chemical imaging 119 

4. P. J. Treado I. W. Levin, E. N. Lewis, Near-Infrared Spectroscopic Imaging Microscopy of Biological Materials 
Using an Infrared Focal -Plane Array and an Acousto-Optic Tunable Filter (AOTF), Applied Spectroscopy, 48:5 
(1994) 

5. Hammond, S.V., Clarke, F. C, Near-infrared microspectroscopy. In: Handbook of Vibrational Spectroscopy, 
Vol. 2, J.M. Chalmers and P.R. Griffiths Eds. John Wiley and Sons, West Sussex, UK, 2002, p.1405-1418 

6. L.H. Kidder, A.S. Haka, E.N. Lewis, Instrumentation for FT-IR Imaging. In: Handbook of Vibrational 
Spectroscopy, Vol. 2, J.M. Chalmers and P.R. Griffiths Eds. John Wiley and Sons, West Sussex, UK, 2002, 
pp. 1386-1404 

7. J. Zhang; A. OGonnor; J. F. Turner II, Cosine Histogram Analysis for Spectral Image Data 
Classification,Applied Spectroscopy, Volume 58, Number 11, November 2004, pp. 1318-1324(7) 

8. J. F. Turner II; J. Zhang; A. O'Connor, A Spectral Identity Mapper for Chemical Image Analysis, Applied 
Spectroscopy, Volume 58, Number 11, November 2004, pp. 1308-1317(10) 

9. H. R. MORRIS, J. F. TURNER II, B. MUNRO, R. A. RYNTZ, P. J. TREADO, Chemical imaging of 
thermoplastic olefin (TPO) surface architecture, Langmuir, 1999, vol. 15, no8, pp. 2961-2972 

10. J. F. Turner II, Chemical imaging and spectroscopy using tunable filters: Instrumentation, methodology, and 
multivariate analysis, Thesis (PhD). UNIVERSITY OF PITTSBURGH, Source DAI-B 59/09, p. 4782, Mar 1999, 
286 pages. 

11. P. Schwille.(2001). in Fluorescence Correlation Spectroscopy. Theory and applications. R. Rigler & E.S. Elson, 
eds., p. 360. Springer Verlag: Berlin. 

12. Schwille P., Oehlenschlager F. and Walter N. (1996). Analysis of RNA-DNA hybridization kinetics by 
fluorescence correlation spectroscopy, Biochemistry 35:10182. 

13. FLIM I Fluorescence Lifetime Imaging Microscopy: Fluorescence, fluorophore chemical imaging, confocal 

[251 
emission microspectroscopy, FRET, cross-correlation fluorescence microspectroscopy 
[251 

14. FLIM Applications: "FLIM is able to discriminate between fluorescence emanating from different 

fluorophores and autoflorescing molecules in a specimen, even if their emission spectra are similar. It is, 
therefore, ideal for identifying fluorophores in multi-label studies. FLIM can also be used to measure intracellular 
ion concentrations without extensive calibration procedures (for example, Calcium Green) and to obtain 
information about the local environment of a fluorophore based on changes in its lifetime." FLIM is also often 
used in microspectroscopic/chemical imaging, or microscopic, studies to monitor spatial and temporal 
protein-protein interactions, properties of membranes and interactions with nucleic acids in living cells. 

15. Gadella TW Jr., FRET and FLIM techniques, 33. Imprint: Elsevier, ISBN 978-0-08-054958-3. (2008) 560 pages 

16. Langel FD, et al., Multiple protein domains mediate interaction between BcllO and Maltl, J. Biol. Chem., 
(2008)283(47):32419-31 

17. Clayton AH. , The polarized AB plot for the frequency-domain analysis and representation of fluorophore 
rotation and resonance energy homotransfer. J Microscopy. (2008) 232(2):306-12 

18. Clayton AH, et al., Predominance of activated EGFR higher-order oligomers on the cell surface. Growth 
Factors (2008) 20:1 

19. Plowman et al., Electrostatic Interactions Positively Regulate K-Ras Nanocluster Formation and Function. 
Molecular and Cellular Biology (2008) 4377-4385 

20. Belanis L, et al., Galectin-1 Is a Novel Structural Component and a Major Regulator of H-Ras Nanoclusters. 
Molecular Biology of the Cell (2008) 19:1404-1414 

21. Van Manen HJ, Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime 
imaging microscopy. Biophys J. (2008) 94(8):L67-9 

22. Van der Krogt GNM, et al., A Comparison of Donor- Acceptor Pairs for Genetically Encoded FRET Sensors: 
Application to the Epac cAMP Sensor as an Example, PLoS ONE, (2008) 3(4):el916 

23. Dai X, et al., Fluorescence intensity and lifetime imaging of free and micellar-encapsulated doxorubicin in 
living cells. Nanomedicine. (2008) 4(l):49-56. 



Chemical imaging 120 

External links 

• NIR Chemical Imaging in Pharmaceutical Industry 

• Pharmaceutical Process Analytical Technology: 



• NIR Chemical Imaging for Counterfeit Pharmaceutical Product Analysis 

[271 

• Chemical Imaging: Potential New Crime Busting Tool 

T281 

• Applications of Chemical Imaging in Research 

References 

[I] http://www.imaging.net/chemical-imaging/Chemical imaging 

[2] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining 

Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004. 
[3] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine., 

doi:10.1146/annurev.anchem.l.031207. 112754 Annual Review of Analytical Chemistry, 1: 883-909. 
[4] Diaspro, A., and Robello, M. (1999). Multi-photon Excitation Microscopy to Study Biosystems. European Microscopy and Analysis., 5:5-7. 
[5] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy., Microchimica Acta, 104, (1-6) 

January 1991, doi: 10.1007/BF01245536 
[6] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of 

binary phospholipid mixtures. Biophys J., 78:290-305. 
[7] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by fluorescence correlation 

spectroscopy with one- and two-photon excitation. Biophysical Journal, 77(10):2251-2265. 
[8] l.Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213. 
[9] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High Resolution Nuclear Magnetic 

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. 

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL. 
[10] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy. 2004.1. 

C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban, q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006) 

[II] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. Laboratory 
Journal Europe, No. 1-2, 2007. 

[12] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY. 

[13] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology. (June 2004) I. C. Baianu, P. R. Lozano, V. I. 

Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047) 
[14] http://www.spectroscopyeurope.com/NIR_14_3.pdf 
[15] http://www.fda.gov/cder/OPS/PAT.htm 
[16] Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary biotechnology, Proc. Natl. Acad. 

Sci. USA 91:5740. 
[17] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy, BioScience (Ed. 

Klinge & Owman) p. 180. 
[18] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy. 2004.1. 

C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006) 
[19] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based amplification combined with 

fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281. 
[20] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High Resolution Nuclear Magnetic 

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. 

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL. 
[21] M. Chamberland, V. Farley, A. Vallieres, L. Belhumeur, A. Villemaire, J. Giroux et J. Legault, High-Performance Field-Portable Imaging 

Radiometric Spectrometer Technology For Hyperspectral imaging Applications, Proc. SPIE 5994, 59940N, September 2005. 
[22] Novel Techniques for Microspectroscopy and Chemical Imaging Analysis of Soybean Seeds and Embryos. (2002). Baianu, I.C, Costescu, 

D.M., and You, T. Soy2002 Conference, Urbana, Illinois. 
[23] Near Infrared Microspectroscopy, Chemical Imaging and NMR Analysis of Oil in Developing and Mutagenized Soybean Embryos in 

Culture. (2003). Baianu, I.C, Costescu, D.M., Hofmann, N., and Korban, S.S. AOCS Meeting, Analytical Division. 
[24] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High Resolution Nuclear Magnetic 

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis. , D. 

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL. 
[25] http://www.nikoninstruments.com/infocenter.php?n=FLIM 
[26] httpV/www.spectroscopymag.com/spectroscopy/Near-IR+Spectroscopy/NIR-Chemical-Imaging-for-Counterfeit-Pharmaceutica/ 

ArticleStandard/Article/detail/406629 



Chemical imaging 121 

[27] http://www. sciencedaily. com/releases/2007/08/070802 1 03435 .htm 

[28] http://www3.imperial.ac.uk/vibrationalspectroscopyandchemicalimaging/research 



Spin polarization 



Spin polarization is the degree to which the spin, i.e. the intrinsic angular momentum of elementary particles, is 
aligned with a given direction . This property may pertain to the spin, hence to the magnetic moment, of 
conduction electrons in ferromagnetic metals, such as iron, giving rise to spin polarized currents. It may also pertain 
to beams of particles, produced for particular aims, such as polarized neutron scattering or muon spin spectroscopy. 
Spin polarization of electrons or of nuclei, often called simply magnetization, is also produced by the application of a 
magnetic field, thanks to the Curie law and it is used to produce an induction signal in Electron spin resonance (ESR 
or EPR) and in Nuclear magnetic resonance (NMR). 

Spin polarization is also important for spintronics, a branch of electronics. Magnetic semiconductors are being 
researched as possible spintronics materials. 

The spin of free electrons is measured either by a LEED image from a clean wolfram-crystal (SPLEED) or 

by an electron microscope composed purely of electrostatic lenses and a gold foil as a sample. Back scattered 
electrons are decelerated by annular optics and focused onto a ring shaped electron mulitplier at about 15°. The 
position on the ring is recorded. This whole device is called a Mott-detector. Depending on their spin the electrons 
have the chance to hit the ring at different positions. 1% of the electrons are scattered in the foil. Of these 1% are 
collected by the detector and then about 30% of the electrons hit the detector at the wrong position. Both devices 
work due to spin orbit coupling. 

References 

[1] J. Kessler (1976). Polarized Electrons. Springer Verlag Berlin Heidelberg, pp. 7—19. 

[2] J. Kirschner and R. Feder (1979). "Spin Polarization in Double Diffraction of Low-Energy Electrons from W(001): Experiment and Theory". 

Physical Review Letters 42: 1008-1011. 
[3] M. Kalisvaart, M. R. O'Neill, T. W. Riddle, F. B. Dunning, and G. K. Walters (1977). "Electron-spin polarization in low-energy electron 

diffraction from tungsten (001)". Physical Review B 17: 1570-1578. 
[4] R. Feder (1976). "Spin Polarization in Low-Energy Electron Diffraction from W(001)". Physical Review Letters 36: 598—600. 



Polarized Neutron Spectroscopy 122 



Polarized Neutron Spectroscopy 



Triple-axis spectrometry (TAS, T also resolved as "three", S also resolved as "spectroscopy") is a technique used in 
inelastic neutron scattering. The instrument is referred to as triple-axis spectrometer (also called TAS). It allows 
measurement of the scattering function at any point in energy and momentum space physically accessible by the 
spectrometer. 

History 

The triple-axis spectrometry method was first developed by Bertram Brockhouse at the NRX research reactor at the 
Chalk River Laboratories in Canada. The first results from the prototype triple-axis spectrometer were published in 
January 1955 and the first true triple-axis spectrometer was built in 1956. Bertram Brockhouse shared the 1994 
Nobel prize for Physics for this development, which allowed elementary excitations, such as phonons and magnons, 
to be observed directly. The Nobel citation was "for pioneering contributions to the development of neutron 
scattering techniques for studies of condensed matter" and "for the development of neutron spectroscopy". 

TAS Instruments in current use 

FRM-II Forschungsneutronenquelle Heinz Maier-Leibnitz 

• PANDA - a cold neutron triple-axis spectrometer. 

• PUMA - a thermal neutron triple-axis spectrometer with multianalyser-detector option. 

Institut Laue-Langevin 

INI - a hot neutron triple-axis spectrometer. 

Mi 
IN3 - a thermal neutron triple-axis spectrometer for tests. 

IN8 - a high-flux thermal neutron triple-axis spectrometer. 

IN 12 - a cold neutron triple-axis spectrometer. 

IN14 - a cold neutron triple-axis spectrometer with polarized neutron capability. 

ro] 

IN20 - a thermal neutron triple-axis spectrometer with polarized neutron capability. 
IN22 - a thermal neutron triple-axis spectrometer with polarized neutron capability. 
D10 - a thermal neutron four-circle diffractometer with a triple-axis energy analysis option. 

CEA/Saclay Laboratoire Leon Brillouin 

• 1T-1 - a double-focusing thermal neutron triple-axis spectrometer. 

• 2T-1 - a thermal neutron triple-axis spectrometer. 

ri3i 

• 4F-1 - a cold neutron triple-axis spectrometer. 

• 4F-2 - a cold neutron triple-axis spectrometer. 

NIST Center for Neutron Research 

• SPINS - a cold neutron triple-axis spectrometer with polarized neutron capability. 

• BT-7 - a thermal neutron triple-axis spectrometer with polarized neutron capability. 



BT-9 - a thermal neutron triple-axis spectrometer. 



Polarized Neutron Spectroscopy 123 

MURR [17] University of Missouri Research Reactor 

• Triax - a thermal neutron triple-axis spectrometer. 

External links 

ri9i 

• Nobelprize.org page for the 1994 Nobel Prize for Physics 

References 

[I] http://wwwnew.frm2.tum.de/en/science/instruments/spectrometers/panda.html 
[2] http://wwwnew.frm2.tum.de/en/science/instruments/spectrometers/puma.html 
[3] http://www.ill.fr/YellowBook/INl/ 

[4] http://www.ill.fr/YellowBook/IN3/ 
[5] http://www.ill.fr/YellowBook/IN8/ 
[6] http://www.ill.fr/YellowBook/IN12/ 
[7] http://www.ill.fr/YellowBook/IN14/ 
[8] http://www.ill.fr/YellowBook/IN20/ 
[9] http://www.ill.fr/YellowBook/IN22/ 
[10] http://www.ill.fr/YellowBook/D10/ 

[II] http://www-llb.cea.fr/spectros/pdf/ltl-llb.pdf 
[12] http://www-llb.cea.fr/spectros/pdf/2tl-llb.pdf 
[13] http ://www-llb.cea. fr/spectros/pdf/4f 1 -lib. pdf 
[14] http://www-llb.cea.fr/spectros/pdf/4f2-llb.pdf 
[15] http://www.ncnr.nist.gov/instruments/spins/ 
[16] http ://www. ncnr.nist. gov/instruments/bt7_new/ 
[17] http://www.murr.missouri.edu/ 

[18] http://www.murr.missouri.edu/rd_material_sciences_instrumentation_triax.php 
[19] http://nobelprize.org/nobel_prizes/physics/laureates/1994/ 



Polarized Muon Spectroscopy 124 



Polarized Muon Spectroscopy 



Muon spin spectroscopy is an experimental technique based on the implantation of spin polarized muons in matter 
and on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. The 
motion of the muon spin is due to the magnetic field experienced by the particle and may provide information on its 
local environment in a very similar way to other magnetic resonance techniques, such as electron spin resonance 
(ESR or EPR) and, more closely, nuclear magnetic resonance (NMR). 

Acronym 

In analogy with the acronyms for these previously established spectroscopies, the muon spin spectroscopy is also 
known as |jSR, which stands for muon spin rotation, or relaxation, or resonance, depending respectively on whether 
the muon spin motion is predominantly a rotation (more precisely a precession around a still magnetic field), or a 
relaxation towards an equilibrium direction, or, again, a more complex dynamics dictated by the addition of short 
radio frequency pulses. 

How it works 

The time scale on which the spin motion may be exploited is that of the muon decay, i.e. a few mean lifetimes, each 
roughly 2.2 ps (2.2 millionths of a second). Both the production of muon beams with nearly perfect alignment of the 
spin to the beam direction (what was referred to above as spin polarization and caused by the spontaneous symmetry 
breaking), and the ability to detect the muon spin direction at the instant of the muon decay rely on the violation of 
parity, which takes place whenever weak forces are at play. 

In short this means that certain elementary events happen only when including clockwise (or only when including 
counterclockwise) rotations. For instance, the positive muon decays into a positron plus two neutrinos and the 
positron is preferentially emitted in the direction of the muon spin. Therefore it would most often see the spin as a 
counterclockwise rotation while flying away from the decay point. 

Spin alignment allows the production of a muon beam with an aligned magnetic moment. Muons are injected into 
the material under investigation as short-lived spies [1] sending information from the interior back out to the 
experimental apparatus. These muons are able to send a message from inside the crystal about the local magnetic 
field in their surroundings. After some time (mean lifetime 2.2 |is) these spies decay and emit positrons. A beam of 
aligned muons produces asymmetric positron radiation. The asymmetry of positron radiation contains information 
about the direction of local magnetic field in the moment of muon decay. Taking into consideration the initial 
direction of muon magnetic moment and the time interval between the moment of injection and moment of muon 
decay we can calculate the precession frequency (how rapidly the muon's magnetic moment rotates). The frequency 
of magnetic moment precession depends on the local magnetic field. Larmor precession is appeared with z -direction 
magnetic field and only decay in 2.2 ps. But when x-direction magnetic field is applied in muon, the rate of decay is 
enhanced by gaussian with depolarization rate. 

Since 1987 this method was used to measure internal magnetic fields inside high-temperature superconductors. 
High-temperature superconductors are Type II superconductors, in which the local magnetic fields inside the 
superconductor depend on the superconducting carrier density — one of the significant parameters of any 
superconductor (see for example the Bardeen— Cooper— Shrieffer theory of superconductors). 



Polarized Muon Spectroscopy 125 

Applications 

Muon Spin Rotation and Relaxation are mostly performed with positive muons. They are well suited to the study of 
magnetic fields at the atomic scale inside matter, such as those produced by various kinds of magnetism and/or 
superconductivity encountered in compounds occurring in nature or artificially produced by modern material 
science. 

The London penetration depth is one of the most important parameters characterizing a superconductor because its 
inverse square provides a measure of the density n of Cooper pairs. The dependence of n on temperature and 
magnetic field directly indicates the symmetry of the superconducting gap. Muon spin spectroscopy provides a way 
to measure the penetration depth, and so has been used to study high-temperature cuprate superconductors since their 
discovery in 1986. 

Other important fields of application of pSR exploit the fact that positive muons capture electrons to form muonium 
atoms which behave chemically as light isotopes of the hydrogen atom. This allows investigation of the largest 
known "isotope effect" in some of the simplest types of chemical reactions, as well as the early stages of formation 
of radicals in organic chemicals. Muonium is also studied as an analogue of hydrogen in semiconductors, where 
hydrogen is one of the most ubiquitous impurities. 

Facilities 

|jSR requires a particle accelerator for the production of a muon beam. This is presently achieved at few large scale 

facilities in the world: the CMMS[2] continuous source at TRIUMF in Vancouver, Canada; the LMU continuous 

mi 
source at the Paul Scherrer Institut (PSI) in Villigen, Switzerland; the ISIS and RIKEN-RAL pulsed sources at the 

Rutherford Appleton Laboratory in Chilton, United Kingdom; and the J-PARC facility in Tokai, Japan, where a new 

pulsed source is being built to replace that at KEK in Tsukuba, Japan. Muon beams are also available at the 

Laboratory of Nuclear Problems, Joint Institute for Nuclear Research (JINR) in Dubna, Russia. The International 

Society for uSR Spectroscopy (ISMS ) exists to promote the worldwide advancement of pSR. Membership in the 

society is open free of charge to all individuals in academia, government laboratories and industry who have an 

interest in the society's goals. 

See also 

• Muon 

• Muonium 

• Nuclear magnetic resonance 

References 

• ISIS Introductory course in pSR 

• introduction to pSR 

• |jSR Brochure [8] (a 3.2 MB PDF file) 

• CMMS [2] : TRIUMF Center for Molecular and Materials Science 

• ISIS [9] 



Polarized Muon Spectroscopy 126 

References 

[1] http://musr.org/intro/musr/ 

[2] http://musr.org/ 

[3] http://lmu.web.psi.ch/ 

[4] http://nectar.nd.rl.ac.uk/~rikenral/index.html 

[5] http://musr.org/isms/ 

[6] http://www.isis. rl.ac.uk/muons/index.htm?content_area=/muons/trainingcourse/course2005.htm&side_nav=/muons/muonsSideNav. 

htm 

[7] http://musr.org/intro/musr/intro.htm 

[8] http://muon.neutron-eu.net/muon/files/muSRBrochure.pdf 

[9] http://www.isis.stfc.ac.uk/ 



Time- resolved spectroscopy 



In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials or 
chemical compounds by means of spectroscopic techniques. Most often, processes are studied that occur after 
illumination of a material, but in principle, the technique can be applied to any process which leads to a change in 
properties of a material. With the help of pulsed lasers, it is possible to study processes which occur on time scales as 

— 14 

short as 10 seconds. The rest of the article discusses different types of time-resolved spectroscopy. 

Transient-absorption spectroscopy 

Transient-absorption spectroscopy is an extension of absorption spectroscopy. Here, the absorbance at a particular 
wavelength or range of wavelengths of a sample is measured as a function of time after excitation by a flash of light. 
In a typical experiment, both the light for excitation ('pump') and the light for measuring the absorbance ('probe') are 
generated by a pulsed laser. If the process under study is slow, then the time resolution can be obtained with a 
continuous (i.e., not pulsed) probe beam and repeated conventional spectrophotometric techniques. 

Examples of processes that can be studied: 

• Optical gain spectroscopy of semiconductor laser materials. 

• Chemical reactions that are initiated by light (or 'photoinduced chemical reactions'); 

• The transfer of excitation energy between molecules, parts of molecules, or molecules and their environment; 

• The behaviour of electrons that are freed from a molecule or crystalline material. 

Other multiple-pulse techniques 

Transient spectroscopy as discussed above is a technique that involves two pulses. There are many more techniques 
that employ two or more pulses, such as: 

• Photon echoes. 

• Four-wave mixing (involves three laser pulses) 

The interpretation of experimental data from these techniques is usually much more complicated than in 
transient-absorption spectroscopy. 

Nuclear magnetic resonance and electron spin resonance are often implemented with multiple-pulse techniques, 
though with radio waves and micro waves instead of visible light. 



Time-resolved spectroscopy 127 

Time-resolved infrared spectroscopy 

Time-resolved infrared (TRIR) spectroscopy also employs a two-pulse, "pump-probe" methodology. The pump pulse 
is typically in the UV region and is often generated by a high-powered Nd:YAG laser whilst the probe beam is in the 
infrared region. This technique currently operates down to the picosecond time regime and surpasses transient 
absorption and emission spectroscopy by providing structural information on the excited-state kinetics of both dark 
and emissive states. 

Time-resolved fluorescence spectroscopy 

Time-resolved fluorescence spectroscopy is an extension of fluorescence spectroscopy. Here, the fluorescence of a 
sample is monitored as a function of time after excitation by a flash of light. The time resolution can be obtained in a 
number of ways, depending on the required sensitivity and time resolution: 

• With fast detection electronics (nanoseconds and slower); 

• With a streak camera (picoseconds and slower); 

• With optical gating (femtoseconds-nanoseconds) - a short laser pulse acts as a gate for the detection of 
fluorescence light; only fluorescence light that arrives at the detector at the same time as the gate pulse is 
detected. This technique has the best time resolution, but the efficiency is rather low. An extension of this optical 
gating technique is to use a "Kerr gate", which allows the scattered Raman signal to be collected before the 
(slower) fluorescence signal overwhelms it. This technique can greatly improve the signaknoise ratio of Raman 
spectra. 



Terahertz spectroscopy 



Terahertz frequency radiation for spectroscopy is typically generated in one of three ways: 

• time domain terahertz spectroscopy (TDTS), using ultrashort laser pulses 

• photomixing, mixing two radiation sources to generate their difference frequency 

• Fourier transform spectroscopy, using a blackbody radiation source 



Applied spectroscopy 



128 



Applied spectroscopy 



Applied spectroscopy is the application of various spectroscopic methods for detection and identification of 
different elements/compounds in solving problems in the fields of forensics, medicine, oil industry, atmospheric 
chemistry, pharmacology, etc. 

Spectroscopic methods 

Among the more common spectroscopic methods used for analysis is FTIR spectroscopy, where chemical bonds can 
be detected through their characteristic infra-red absorption frequencies or wavelengths. UV spectroscopy is used 
where strong absorption of ultra-violet radiation occurs in a substance. Such groups are known as chromophores and 
include aromatic groups, conjugated system of bonds, carbonyl groups and so on. NMR spectroscopy detects 
hydrogen atoms in specific environments, and complements both IR and UV spectroscopy. The use of Raman 
spectroscopy is growing for more specialist applications. 

There are also derivative methods such as infrared microscopy which allows very small areas to be analysed in an 
optical microscope. 

One method of elemental analysis which is important in forensic analysis is EDX performed in the environmental 
scanning electron microscope, or ESEM. The method involves analysis of back-scattered X-rays from the sample as 
a result of interaction with the electron beam. 

Sample preparation 

In all three spectroscopic methods, the sample usually needs to be present in solution, which may present problems 
during forensic examination because it necessarily involves sampling solid from the object to be examined. 

FTIR: Three types of samples can be analyzed, a solution (KBr), a powder, or a film. A solid film is the easiest and 
most straight forward sample type to test. 

Analysis of polymers 

Many polymer degradation mechanisms can be followed using infra-red spectroscopy, such as UV degradation and 
oxidation, amongst many other failure modes. 



UV degradation 

Many polymers are attacked by UV radiation at vulnerable points 
in their chain structures. Thus polypropylene suffers severe 
cracking in sunlight unless anti-oxidants are added. The point of 
attack occurs at the tertiary carbon atom present in every repeat 
unit, causing oxidation and finally chain breakage. Polyethylene is 
also susceptible to UV degradation, especially those variants 
which are branched polymers such as LDPE. The branch points 
are tertiary carbon atoms, so polymer degradation starts there and 
results in chain cleavage, and embrittlement. In the example 
shown at left, carbonyl groups were readily detected by IR 

spectroscopy from a cast thin film. The product was a road cone which had cracked in service, and many similar 

cones also failed because an anti-UV additive had not been used. 



\ 


r 


/ 


C-0 






/ 







1400 1200 1000 

WavG Number (cm -1 ) 



IR spectrum showing carbonyl absorption due to UV 
degradation of polyethylene 



Applied spectroscopy 



129 



Oxidation 

Polymers are susceptible to attack by atmospheric oxygen, 
especially at elevated temperatures encountered during processing 
to shape. Many process methods such as extrusion and injection 
moulding involve pumping molten polymer into tools, and the 
high temperatures needed for melting may result in oxidation 
unless precautions are taken. For example, a forearm crutch 
suddenly snapped and the user was severely injured in the 
resulting fall. The crutch had fractured across a polypropylene 
insert within the aluminium tube of the device, and infra-red 
spectroscopy of the material showed that it had oxidised, possible 
as a result of poor moulding. 




4000 3500 3000 2500 2000 



IR spectrum showing carbonyl absorption due to 

oxidative degradation of polypropylene crutch 

moulding 



Oxidation is usually relatively easy to detect owing to the strong 

absorption by the carbonyl group in the spectrum of polyolefins. 

Polypropylene has a relatively simple spectrum with few peaks at the carbonyl position (like polyethylene). 

Oxidation tends to start at tertiary carbon atoms because free radicals here at more stable, so last longer and are 

attacked by oxygen. The carbonyl group can be further oxidised to break the chain, so weakening the material by 

lowering the molecular weight, and cracks start to grow in the regions affected. 



Ozonolysis 

The reaction occurring between double bonds and ozone is known as ozonolysis when one molecule of the gas reacts 
with the double bond: 



RjR 3 o 3 

/=\ ; 

R 2 R 4 



R-i R3 

R 2 R4 



The immediate result is formation of an ozonide, which then decomposes rapidly so that the double bond is cleaved. 
This is the critical step in chain breakage when polymers are attacked. The strength of polymers depends on the 
chain molecular weight or degree of polymerization, the higher the chain length, the greater the mechanical strength 
(such as tensile strength). By cleaving the chain, the molecular weight drops rapidly and there comes a point when it 
has little strength whatsoever, and a crack forms. Further attack occurs in the freshly exposed crack surfaces and the 
crack grows steadily until it completes a circuit and the product separates or fails. In the case of a seal or a tube, 
failure occurs when the wall of the device is penetrated. 



Applied spectroscopy 



130 



•:.li- 




|j 












40-; 




' 












3D— 




| 












?n_ 






















& 


S 








10-= 




JIJ 


Jl Al 














I 






hi _Ci 




Zr, 



















EDX spectrum of crack surface 



20- 


D 


\5— 












s 


10— 






a 




5- 






H 3 n 




!■■■ ' 




^rrrrrrrr7rr^T. r 7^ a i 



EDX spectrum of unaffected rubber surface 



The carbonyl end groups which are formed are usually 
aldehydes or ketones, which can oxidise further to 
carboxylic acids. The net result is a high concentration 
of elemental oxygen on the crack surfaces, which can 
be detected using Energy-dispersive X-ray 
spectroscopy in the environmental SEM, or ESEM. The 
spectrum at left shows the high oxygen peak compared 
with a constant sulphur peak. The spectrum at right 
shows the unaffected elastomer surface spectrum, with 
a relatively low oxygen peak compared with the 
sulphur peak. The spectra were obtained during an 
investigation into ozone cracking of diaphragm seals in 
a semi-conductor fabrication factory. 

See also 

Absorption spectroscopy 

Infrared spectroscopy correlation table 

Infrared spectroscopy 

Forensic chemistry 

Forensic engineering 

Forensic polymer engineering 

Polymer degradation 

Polymer engineering 

Spectroscopy 



• Society for Applied Spectroscopy 

References 

• Forensic Materials Engineering: Case Studies by Peter Rhys Lewis, Colin Gagg, Ken Reynolds, CRC Press 
(2004). 

• Peter R Lewis and Sarah Hainsworth, Fuel Line Failure from stress corrosion cracking, Engineering Failure 
Analysis, 13 (2006) 946-962. 



External links 

• Museum of failed products 

• New Forensic course 



[l] 



The journal Engineering Failure Analysis 



[3] 



Forensic science and engineering 



[4] 



Applied spectroscopy 



131 



References 

[1] http://materials.open.ac.uk/mem/index.htm 

[2] http://openlearn.open.ac.uk/file.php/2980/formats/print.htm 

[3] http://www.elsevier.eom/wps/find/journaldescription.cws_home/30190/description#description 

[4] http://www. forensic-courses. com/wordpress/?p=42; 



Amino acids 



Amino acids are molecules containing an 
amine group, a carboxylic acid group and a side 
chain that varies between different amino acids. 
These molecules contain the key elements of 
Carbon, Hydrogen, Oxygen, and Nitrogen. 
These molecules are particularly important in 
biochemistry, where this term refers to 
alpha-amino acids with the general formula 
H 2 NCHRCOOH, where R is an organic 
substituent. In an alpha amino acid, the amino 
and carboxylate groups are attached to the same 
carbon atom, which is called the a— carbon. The 
various alpha amino acids differ in which side 
chain (R group) is attached to their alpha 
carbon. These side chains can vary in size from 
just a hydrogen atom in glycine, to a methyl 
group in alanine, through to a large heterocyclic 
group in tryptophan. 

Amino acids are critical to life, and have many 
functions in metabolism. One particularly 
important function is as the building blocks of 
proteins, which are linear chains of amino acids. 
Every protein is chemically defined by this 
primary structure, its unique sequence of amino 
acid residues, which in turn define the 
three-dimensional structure of the protein. Just 
as the letters of the alphabet can be combined to 
form an almost endless variety of words, amino 
acids can be linked together in varying 
sequences to form a vast variety of proteins. 
Amino acids are also important in many other 
biological molecules, such as forming parts of 
coenzymes, as in S-adenosylmethionine, or as 
precursors for the biosynthesis of molecules 
such as heme. Due to this central role in 
biochemistry, amino acids are very important in 




Twenty-One Amino Acids 



A. Amino Adds with Bemicaly Charged Side Chains 
Positive 





6, flm-inc Grid's witfr Palar Uncharged Side Chains C Speaal Cases 

Serine Threonine Asparagine Glutamine Cysteine 5elenocystelne Glycine Proline 

' :x '"0 <Thl> A ,Asnt fl [Ght _!_ '""'''ifft ISecl ffi (Glyt <5_ '"'■ £_ 




D. Amino A;. 1 .:; n/ith htfdiaphobk SWc Chain 

Alanine Isaleucine Leucine Methionine P hen ylaLa nine Tryptophan Tyrosine Valine 




The twenty-one amino acids found in eukaryotes, grouped according to their 
side chains' pKa's and charge at physiological pH 7.4 



Amino acids 132 

nutrition. Amino acids are commonly used in food technology and industry. For example, monosodium glutamate is 
a common flavor enhancer that gives foods the taste called umami. They are also used in industry. Applications 
include the production of biodegradable plastics, drugs and chiral catalysts. 

History 

The first few amino acids were discovered in the early 1800s. In 1806, the French chemists Louis-Nicolas Vauquelin 
and Pierre Jean Robiquet isolated a compound in asparagus that proved to be asparagine, the first amino acid to be 
discovered. Another amino acid that was discovered in the early 19th century was cystine, in 1810, although 

its monomer, cysteine, was discovered much later, in 1884. Glycine and leucine were also discovered around 

mistime, in 1820. [7] 

General structure 



C'OO 



In the structure shown at the top of the page, R represents a side chain specific to 

each amino acid. The carbon atom next to the carbonyl group is called the a— carbon 

and amino acids with a side chain bonded to this carbon are referred to as alpha , ffi J^ -„ 

amino acids. These are the most common form found in nature. In the alpha amino ' i 

T81 ft I 3 

acids, the a— carbon is a chiral carbon atom, with the exception of glycine. In /tT 



amino acids that have a carbon chain attached to the a— carbon (such as lysine, 

[9] 



y I i 



shown to the right) the carbons are labeled in order as a, |3, y, 8, and so on. In CHa 

some amino acids, the amine group is attached to the (3 or y-carbon, and these are § | ^ 

therefore referred to as beta or gamma amino acids. v-Hj 

5 I fl 
Amino acids are usually classified by the properties of their side chain into four £TH 

groups. The side chain can make an amino acid a weak acid or a weak base, and a I 

roi ^^ | 

hydrophile if the side chain is polar or a hydrophobe if it is nonpolar. The Nil- 

chemical structures of the twenty-two standard amino acids, along with their 

Lysine with the carbon atoms in 

chemical properties, are described more fully in the article on these proteinogenic the side chain | abe i e( j 

amino acids. 

The phrase "branched-chain amino acids" or BCAA refers to the amino acids having aliphatic side chains that are 
non-linear; these are leucine, isoleucine, and valine. Proline is the only proteinogenic amino acid whose side group 
links to the a-amino group and, thus, is also the only proteinogenic amino acid containing a secondary amine at this 
position. Chemically, proline is therefore an imino acid since it lacks a primary amino group, although it is still 
classed as an amino acid in the current biochemical nomenclature, and may also be called an "N-alkylated 
alpha-amino acid". 

Isomerism 

Of the standard a-amino acids, all but glycine can exist in either of two 
optical isomers, called L or D amino acids, which are mirror images of 
each other (see also Chirality). While L-amino acids represent all of the 
amino acids found in proteins during translation in the ribosome, 
D-amino acids are found in some proteins produced by enzyme 
posttranslational modification after translation and translocation to the 
endoplasmic reticulum, as in exotic sea-dwelling organisms such as 

The two optical isomers of alanine, D- Alanine ., [131 „. , , , „ ., 

cone snails. They are also abundant components of the 

and L-Alanine 




Amino acids 



133 



peptidoglycan cell walls of bacteria. and D-serine may act as a neurotransmitter in the brain. The L and D 
convention for amino acid configuration refers not to the optical activity of the amino acid itself, but rather to the 
optical activity of the isomer of glyceraldehyde from which that amino acid can theoretically be synthesized 
(D-glyceraldehyde is dextrorotary; L-glyceraldehyde is levorotary). Alternatively, the (S) and (R) designators are 
used to indicate the absolute stereochemistry. Almost all of the amino acids in proteins are (S) at the a carbon, with 
cysteine being (R) and glycine non-chiral. Cysteine is unusual since it has a sulfur atom at the first position in its 
side-chain, which has a larger atomic mass than the groups attached to the a-carbon in the other standard amino 
acids, thus the (R) instead of (S). 



Zwitterions 

Amino acids have both amine and 
carboxylic acid functional groups and 
are therefore both an acid and a base at 

ro] 

the same time. At a certain pH known 
as the isoelectric point an amino acid 
has no overall charge, since the number 
of protonated ammonium groups 
(positive charges) and deprotonated 
carboxylate groups (negative charges) 
are equal. The amino acids all have 
different isoelectric points. The ions produced at the isoelectric point have both positive and negative charges and are 

„ [18] 






H 




© 


H 




H 2 N- 


R 




H 3 N + 


R 


X) 



An amino acid in its (1) unionized and (2) zwitterionic forms 



[19] 



known as a zwitterion, which comes from the German word Zwitter meaning "hermaphrodite" or "hybrid 
Amino acids can exist as zwitterions in solids and in polar solutions such as water, but not in the gas phase. 1 
Zwitterions have minimal solubility at their isolectric point and an amino acid can be isolated by precipitating it from 
water by adjusting the pH to its particular isolectric point. 



Occurrence and functions in biochemistry 



Standard amino acids 

Amino acids are the structural units that 
make up proteins. They join together to 
form short polymer chains called peptides or 
longer chains called either polypeptides or 
proteins. These polymers are linear and 
unbranched, with each amino acid within 
the chain attached to two neighbouring 
amino acids. The process of making proteins 
is called translation and involves the 
step-by-step addition of amino acids to a 
growing protein chain by a ribozyme that is 




Amino Acid 



A polypeptide is an unbranched chain of amino acids. 



called a ribosome. The order in which the 

amino acids are added is read through the genetic code from an mRNA template, which is a RNA copy of one of the 

organism's genes 

Twenty-two amino acids are naturally incorporated into polypeptides and are called proteinogenic or standard amino 

ro] 

acids. Of these twenty-two, twenty are directly encoded by the universal genetic code. The remaining two, 



Amino acids 



134 



selenocysteine and pyrrolysine, are incorporated into proteins by unique synthetic mechanisms. Selenocysteine is 

incorporated when the mRNA being translated includes a SECIS element, which causes the UGA codon to encode 

T211 
selenocysteine instead of a stop codon. Pyrrolysine is used by some methanogenic archaea in enzymes that they 

[221 
use to produce methane. It is coded for with the codon UAG, which is normally a stop codon in other organisms. 



HSe 



Non-standard amino acids 

Aside from the twenty-two standard amino acids, there are a vast 

number of "non-standard" amino acids. These non-standard amino 

acids found in proteins are formed by post-translational modification, 

which is modification after translation in protein synthesis. These 

modifications are often essential for the function or regulation of a 

protein; for example, the carboxylation of glutamate allows for better 

[231 
binding of calcium cations, and the hydroxylation of proline is 

T241 
critical for maintaining connective tissues. Another example is the 

formation of hypusine in the translation initiation factor EIF5A, 

T251 
through modification of a lysine residue. Such modifications can 

also determine the localization of the protein, e.g., the addition of long hydrophobic groups can cause a protein to 

bind to a phospholipid membrane 



HoN 




The amino acid selenocysteine 



[26] 



C^H, 



H a c a 

►H 3 N COO 



+H,N 



cph, 



H 



if \ 



al 



Examples of nonstandard amino acids that are not 
found in proteins include lanthionine, 
2-aminoisobutyric acid, dehydroalanine and the 
neurotransmitter gamma-aminobutyric acid. 

Nonstandard amino acids often occur as intermediates 
in the metabolic pathways for standard amino acids — 
for example ornithine and citrulline occur in the urea 

T271 

cycle, part of amino acid catabolism (see below). A 
rare exception to the dominance of a-amino acids in 
biology is the p-amino acid beta alanine 
(3-aminopropanoic acid), which is used in plants and microorganisms in the synthesis of pantothenic acid (vitamin 



COO 



L-ot alanine ^-alanine 

|3-alanine and its a-alanine isomer 



B5), a component of coenzyme A 



[28] 



In human nutrition 

When taken up into the human body from the diet, the twenty two standard amino acids are either used to synthesize 

[29] 
proteins and other biomolecules or oxidized to urea and carbon dioxide as a source of energy. The oxidation 

pathway starts with the removal of the amino group by a transaminase, the amino group is then fed into the urea 

cycle. The other product of transamidation is a keto acid that enters the citric acid cycle. Glucogenic amino acids 

nil 
can also be converted into glucose, through gluconeogenesis. 

Pyrrolysine trait is restricted to several microbes, and only one organism has both Pyl and Sec. Of the twenty-two 
standard amino acids, eight are called essential amino acids because the human body cannot synthesize them from 

[32] 

other compounds at the level needed for normal growth, so they must be obtained from food. However, the 
situation is quite complicated since cysteine, taurine, tyrosine, histidine and arginine are semiessential amino acids in 
children, because the metabolic pathways that synthesize these amino acids are not fully developed. The 

amounts required also depend on the age and health of the individual, so it is hard to make general statements about 
the dietary requirement for some amino acids. 



Amino acids 



135 



Essential 


Nonessential 


Isoleucine 


Alanine 


Leucine 


Asparagine 


Lysine 


Aspartic Acid 


Methionine 


Cysteine* 


Phenylalanine 


Glutamic Acid 


Threonine 


Glutamine* 


Tryptophan 


Glycine* 


Valine 


Proline* 




Selenocysteine* 




Serine* 




Tyrosine* 




Arginine* 




Histidine* 



(*) Essential only in certain cases 



[35] [36] 



Non-protein functions 

In humans, non-protein amino acids also have important roles as metabolic intermediates, such as in the biosynthesis 
of the neurotransmitter gamma-aminobutyric acid. Many amino acids are used to synthesize other molecules, for 
example: 



Tryptophan is a precursor of the neurotransmitter serotonin 
Glycine is a precursor of porphyrins such as heme 



[37] 



[38] 



Arginine is a precursor of nitric oxide 



[39] 



Ornithine and S-adenosylmethionine are precursors of poly amines 



[40] 



[41] 

• Aspartate, glycine and glutamine are precursors of nucleotides. 

• Phenylalanine is a precursor of various phenylpropanoids which are important in plant metabolism. 

However, not all of the functions of other abundant non-standard amino acids are known, for example taurine is a 
major amino acid in muscle and brain tissues, but although many functions have been proposed, its precise role in 

[421 

the body has not been determined. 

[43] 

Some non-standard amino acids are used as defenses against herbivores in plants. For example canavanine is an 

[441 

analogue of arginine that is found in many legumes, and in particularly large amounts in Canavalia gladiata 

[451 

(sword bean). This amino acid protects the plants from predators such as insects and can cause illness in people if 
some types of legumes are eaten without processing. The non-protein amino acid mimosine is found in other 

[471 

species of legume, particularly Leucaena leucocephala. This compound is an analogue of tyrosine and can poison 
animals that graze on these plants. 



Uses in technology 

Amino acids are used for a variety of applications in industry but their main use is as additives to animal feed. This is 
necessary since many of the bulk components of these feeds, such as soybeans, either have low levels or lack some 
of the essential amino acids: lysine, methionine, threonine, and tryptophan are most important in the production of 

these feeds. The food industry is also a major consumer of amino acids, particularly glutamic acid, which is used 

[491 
as a flavor enhancer, and Aspartame (aspartyl-phenylalanine-1 -methyl ester) as a low-calorie artificial 



Amino acids 



136 



sweetener. The remaining production of amino acids is used in the synthesis of drugs and cosmetics. 



Amino acid derivative 


Pharmaceutical application 


5-HTP (5-hydroxytryptophan) 


Experimental treatment for depression. 


L-DOPA (L-dihydroxyphenylalanine) 


[52] 
Treatment for Parkinsonism. 


Eflornithine 


Drug that inhibits ornithine decarboxylase and is used in the treatment of sleeping sickness 


[53] 



Chemical building blocks 

Amino acids are important as low-cost feedstocks. These compounds are used in chiral pool synthesis as 

[541 

enantiomerically-pure building blocks. 

Amino acids have been investigated as precursors chiral catalysts, e.g. for asymmetric hydrogenation reactions, 
although no commercial applications exist. 

Biodegradable plastics 

Amino acids are under development as components of a range of biodegradable polymers. These materials have 
applications as environmentally-friendly packaging and in medicine in drug delivery and the construction of 
prosthetic implants. These polymers include polypeptides, polyamides, polyesters, poly sulfides and polyurethanes 
with amino acids either forming part of their main chains or bonded as side chains. These modifications alter the 
physical properties and reactivities of the polymers. An interesting example of such materials is poly aspartate, a 

[571 

water-soluble biodegradable polymer that may have applications in disposable diapers and agriculture. Due to its 
solubility and ability to chelate metal ions, polyaspartate is also being used as a biodegradeable anti-scaling agent 
and a corrosion inhibitor. In addition, the aromatic amino acid tyrosine is being developed as a possible 

replacement for toxic phenols such as bisphenol A in the manufacture of polycarbonates. 

Reactions 

As amino acids have both a primary amine group and a primary carboxyl group, these chemicals can undergo most 
of the reactions associated with these functional groups. These include nucleophilic addition, amide bond formation 
and imine formation for the amine group and esterification, amide bond formation and decarboxylation for the 
carboxylic acid group. The multiple side chains of amino acids can also undergo chemical reactions. The types 
of these reactions are determined by the groups on these side chains and are therefore different between the various 
types of amino acid. 



KCN 





R A H NHz CI 



NH 2 



H + 



NH : 



N 




O 



OH 



The Strecker amino acid synthesis 



Chemical synthesis 

Several methods exist to synthesize 
amino acids. One of the oldest 
methods, begins with the bromination 
at the a-carbon of a carboxyic acid. 
Nucleophilic substitution with 
ammonia then converts the alkyl bromide to the amino acid. LUJJ Alternatively, the Strecker amino acid synthesis 
involves the treatment of an aldehyde with potassium cyanide and ammonia, this produces an a-amino nitrile as an 
intermediate. Hydrolysis of the nitrile in acid then yields a a-amino acid. Using ammonia or ammonium salts in 
this reaction gives unsubstituted amino acids, while substituting primary and secondary amines will yield substituted 

amino acids. Likewise, using ketones, instead of aldehydes, gives a,a-disubstituted amino acids. The classical 
synthesis gives racemic mixtures of a-amino acids as products, but several alternative procedures using asymmetric 



[63] 



Amino acids 



137 



Amino acid (1) 



Amino acid (2) 



auxiliaries or asymmetric catalysts have been developed. 

Currently the most adopted method is an automated synthesis on a solid support (e.g. polystyrene beads), using 
protecting groups (e.g. Fmoc and t-Boc) and activating groups (e.g. DCC and DIC). 



Peptide bond formation 

As both the amine and carboxylic acid 
groups of amino acids can react to 
form amide bonds, one amino acid 
molecule can react with another and 
become joined through an amide 
linkage. This polymerization of amino 
acids is what creates proteins. This 
condensation reaction yields the newly 
formed peptide bond and a molecule of 
water. In cells, this reaction does not 
occur directly; instead the amino acid 
is first activated by attachment to a 
transfer RNA molecule through an 
ester bond. This aminoacyl-tRNA is 
produced in an ATP-dependent 
reaction carried out by an aminoacyl 
fRNA synthetase. [71] This 

aminoacyl-tRNA is then a substrate for 
the ribosome, which catalyzes the 
attack of the amino group of the elongatin 
proteins made by ribosomes are synthesized 



▼ H 



Peptide bond 




Water 
Dipeptide 

The condensation of two amino acids to form a peptide bond 



T721 
g protein chain on the ester bond. As a result of this mechanism, all 

starting at their N-terminus and moving towards their C-terminus. 



However, not all peptide bonds are formed in this way. In a few cases, peptides are synthesized by specific enzymes. 
For example, the tripeptide glutathione is an essential part of the defenses of cells against oxidative stress. This 
peptide is synthesized in two steps from free amino acids. In the first step gamma-glutamylcysteine synthetase 
condenses cysteine and glutamic acid through a peptide bond formed between the side-chain carboxyl of the 

glutamate (the gamma carbon of this side chain) and the amino group of the cysteine. This dipeptide is then 

T741 
condensed with glycine by glutathione synthetase to form glutathione. 

In chemistry, peptides are synthesized by a variety of reactions. One of the most used in solid-phase peptide 

synthesis, which uses the aromatic oxime derivatives of amino acids as activated units. These are added in sequence 

[751 
onto the growing peptide chain, which is attached to a solid resin support. The ability to easily synthesize vast 

numbers of different peptides by varying the types and order of amino acids (using combinatorial chemistry) has 

made peptide synthesis particularly important in creating libraries of peptides for use in drug discovery through 

high-throughput screening 



[76] 



Biosynthesis and catabolism 

In plants, nitrogen is first assimilated into organic compounds in the form of glutamate, formed from 

alpha-ketoglutarate and ammonia in the mitochondrion. In order to form other amino acids, the plant uses 

transaminases to move the amino group to another alpha-keto carboxylic acid. For example, aspartate 

[77] 
aminotransferase converts glutamate and oxaloacetate to alpha-ketoglutarate and aspartate. Other organisms use 

transaminases for amino acid synthesis too. Transaminases are also involved in breaking down amino acids. 



Amino acids 138 

Degrading an amino acid often involves moving its amino group to alpha-ketoglutarate, forming glutamate. In many 
vertebrates, the amino group is then removed through the urea cycle and is excreted in the form of urea. However, 
amino acid degradation can produce uric acid or ammonia instead. For example, serine dehydratase converts serine 
to pyruvate and ammonia. 

Nonstandard amino acids are usually formed through modifications to standard amino acids. For example, 
homocysteine is formed through the transsulfuration pathway or by the demethylation of methionine via the 

[421 

intermediate metabolite S-adenosyl methionine, while hydroxyproline is made by a posttranslational modification 
of proline. 

Microorganisms and plants can synthesize many uncommon amino acids. For example, some microbes make 
2-aminoisobutyric acid and lanthionine, which is a sulfide-bridged derivative of alanine. Both of these amino acids 
are found in peptidic lantibiotics such as alamethicin. While in plants, 1-aminocyclopropane-l-carboxylic acid is 

roil 

a small disubstituted cyclic amino acid that is a key intermediate in the production of the plant hormone ethylene. 



Hydrophilic and hydrophobic amino acids 



rsi 
Depending on the polarity of the side chain, amino acids vary in their hydrophilic or hydrophobic character. These 

properties are important in protein structure and protein— protein interactions. The importance of the physical 

properties of the side chains comes from the influence this has on the amino acid residues' interactions with other 

structures, both within a single protein and between proteins. The distribution of hydrophilic and hydrophobic amino 

acids determines the tertiary structure of the protein, and their physical location on the outside structure of the 

ro] 

proteins influences their quaternary structure. 

For example, soluble proteins have surfaces rich with polar amino acids like serine and threonine, while integral 
membrane proteins tend to have outer rings of hydrophobic amino acids that anchor them into the lipid bilayer. In 
the case part-way between these two extremes, peripheral membrane proteins have a patch of hydrophobic amino 
acids on their surface that locks onto the membrane. Similarly, proteins that have to bind to positively-charged 
molecules have surfaces rich with negatively charged amino acids like glutamate and aspartate, while proteins 
binding to negatively-charged molecules have surfaces rich with positively charged chains like lysine and arginine. 
Recently a new scale of hydrophobicity based on the free energy of hydrophobic association has been proposed. 

The hydrophilic and hydrophobic interactions of proteins are not always the result of the properties of their amino 
acid sidechains. This is because a range of posttranslational modifications can attach other chemical groups to the 
amino acids in proteins. For example, these modifications can produce hydrophobic lipoproteins, or hydrophilic 
glycoproteins. These type of modification allow the reversible targeting of a protein to a membrane. For example, 
the addition and removal of the fatty acid palmitic acid to cysteine residues in some signaling proteins causes the 

roc] 

proteins to attach and then detach from cell membranes. 

Table of standard amino acid abbreviations and side chain properties 



Amino acids 



139 



Amino Acid 


3-Letter [86] 


1-Letter [86] 


Side chain 

i •. [ 8fi ] 
polarity 


Side chain charge 

(phW 8 * 


Hydropathy 
index 


Absorbance 

I („m) [88] 
max 


e at X (xlO -3 
M-cZ-V 881 


Alanine 


Ala 


A 


nonpolar 


neutral 


1.8 






Arginine 


Arg 


R 


polar 


positive 


-4.5 






Asparagine 


Asn 


N 


polar 


neutral 


-3.5 






Aspartic acid 


Asp 


D 


polar 


negative 


-3.5 






Cysteine 


Cys 


C 


nonpolar 


neutral 


2.5 


250 


0.3 


Glutamic acid 


Glu 


E 


polar 


negative 


-3.5 






Glutamine 


Gin 


Q 


polar 


neutral 


-3.5 






Glycine 


Gly 


G 


nonpolar 


neutral 


-0.4 






Histidine 


His 


H 


polar 


positive(10%), 
neutral(90%) 


-3.2 


211 


5.9 


Isoleucine 


He 


I 


nonpolar 


neutral 


4.5 






Leucine 


Leu 


L 


nonpolar 


neutral 


3.8 






Lysine 


Lys 


K 


polar 


positive 


-3.9 






Methionine 


Met 


M 


nonpolar 


neutral 


1.9 






Phenylalanine 


Phe 


F 


nonpolar 


neutral 


2.8 


257, 206, 188 


0.2, 9.3, 60.0 


Proline 


Pro 


P 


nonpolar 


neutral 


-1.6 






Serine 


Ser 


S 


polar 


neutral 


-0.8 






Threonine 


Thr 


T 


polar 


neutral 


-0.7 






Tryptophan 


Trp 


W 


nonpolar 


neutral 


-0.9 


280,219 


5.6, 47.0 


Tyrosine 


Tyr 


Y 


polar 


neutral 


-1.3 


274, 222, 193 


1.4,8.0,48.0 


Valine 


Val 


V 


nonpolar 


neutral 


4.2 







In addition to the specific amino acid codes, placeholders are used in cases where chemical or crystallographic 
analysis of a peptide or protein can not conclusively determine the identity of a residue. 



Ambiguous Amino Acids 

Asparagine or aspartic acid 



Glutamine or glutamic acid 
Leucine or Isoleucine 



3-Letter 


1 -Letter 


Asx 


B 


Glx 


Z 


Xle 


J 



Unspecified or unknown amino acid Xaa 



Unk is sometimes used instead of Xaa, but is less standard. 

Additionally, many non-standard amino acids have a specific code. For example, several peptide drugs, such as 
Bortezomib or MG132 are artificially synthesized and retain their protecting groups, which have specific codes. 
Bortezomib is Pyz-Phe-boroLeu and MG132 is Z-Leu-Leu-Leu-al. Additionally, To aid in the analysis of protein 
structure, photocros slinking amino acids are available. These include photoleucine (pLeu) and photomethionine 



(pMet) 



[891 



Amino acids 140 

See also 

Amino acid dating 

Beta amino acid 

Degron 

Glucogenic amino acid 

Homochirality 

Leucines 

Proteinogenic amino acid (including chemical structures) 

Table of codons, 3-nucleotide sequences that encode each amino acid 

Further reading 

• Doolittle, R.F. (1989) Redundancies in protein sequences. In Predictions of Protein Structure and the Principles 
of Protein Conformation (Fasman, G.D. ed) Plenum Press, New York, pp. 599—623 

• David L. Nelson and Michael M. Cox, Lehninger Principles of Biochemistry, 3rd edition, 2000, Worth Publishers, 
ISBN 1-57259-153-6 

• Meierhenrich, U.J.: Amino acids and the asymmetry of life, Springer- Verlag, Berlin, New York, 2008. ISBN 
978-3-540-76885-2 

• Morelli, Robert J. "Studies of amino acid absorption from the small intestine." San Francisco: Morelli, 1952. 

External links 

• Amino acids overview physical-chemistry properties, 3D structures, etc 

• List of Standard Amino Acids The Detailed PDF List of Standard Amino Acids (including 3D depictions) 

[92] 

• Nomenclature and Symbolism for Amino Acids and Peptides IUPAC-IUB Joint Commission on Biochemical 



[93] 
Molecular Expressions: The Amino Acid Collection — Has detailed information and microscopy photographs 

[94] 
• Amino acid properties — Properties of the amino acids (a tool aimed mostly at molecular geneticists trying to 



Nomenclature (JCBN) 

Molecular Expressi 

of each amino acid 

Amino acid propen 

understand the meaning of mutations) 

[95] 

• Synthesis of Amino Acids and Derivatives 

• Learn the 20 proteinogenic amino acids online 

[97] 

• The origin of the single-letter code for the amino acids 

• Amino acid solution's pH, titration and isoelectric point calculation free spreadsheet 

References 

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Proteins 



144 



Proteins 





This 



article is part of the series on: 
Gene expression 

a Molecular biology topic {portal) 
(Glossary) 



Introduction to Genetics 

General flow: DNA > RNA > Protein 



special transfers (RNA > RNA, 
RNA > DNA, Protein > Protein) 

Genetic code 



Transcription 

Transcription (Transcription factors, 
RNA Polymerase, promoter) Prokaryotic / Archaeal / Eukaryotic 



post-transcriptional modification 
(hnRNA,Splicing) 

Translation 



Translation (Ribosome,tRNA) Prokaryotic / Archaeal / Eukaryotic 

post-translational modification 

{functional groups, peptides, 

structural changes) 



gene regulation 

epigenetic regulation 
{Genomic imprinting) 



transcriptional regulation 

post-transcriptional regulation 

{sequestration, 

alternative splicing, miRN A) 



translational regulation 

post-translational regulation 
(reversible irreversible) 



[1] ,- [2] 
ask a question , edit 



Proteins 



145 




A representation of the 3D structure of myoglobin 

showing coloured alpha helices. This protein was the 

first to have its structure solved by X-ray 

crystallography. 



Proteins (also known as polypeptides) are organic compounds 
made of amino acids arranged in a linear chain and folded into a 
globular form. The amino acids in a polymer are joined together 
by the peptide bonds between the carboxyl and amino groups of 
adjacent amino acid residues. The sequence of amino acids in a 
protein is defined by the sequence of a gene, which is encoded in 
the genetic code. In general, the genetic code specifies 20 
standard amino acids; however, in certain organisms the genetic 
code can include selenocysteine — and in certain 
archaea — pyrrolysine. Shortly after or even during synthesis, the 
residues in a protein are often chemically modified by 
post-translational modification, which alters the physical and 
chemical properties, folding, stability, activity, and ultimately, the 
function of the proteins. Proteins can also work together to achieve 
a particular function, and they often associate to form stable 
complexes 



[4] 



Like other biological macromolecules such as polysaccharides and 
nucleic acids, proteins are essential parts of organisms and 
participate in virtually every process within cells. Many proteins are enzymes that catalyze biochemical reactions 
and are vital to metabolism. Proteins also have structural or mechanical functions, such as actin and myosin in 
muscle and the proteins in the cytoskeleton, which form a system of scaffolding that maintains cell shape. Other 
proteins are important in cell signaling, immune responses, cell adhesion, and the cell cycle. Proteins are also 
necessary in animals' diets, since animals cannot synthesize all the amino acids they need and must obtain essential 
amino acids from food. Through the process of digestion, animals break down ingested protein into free amino acids 
that are then used in metabolism. 

Proteins were first described by the Dutch chemist Gerhardus Johannes Mulder and named by the Swedish chemist 
Jons Jakob Berzelius in 1838. The central role of proteins in living organisms was however not fully appreciated 
until 1926, when James B. Sumner showed that the enzyme urease was a protein. The first protein to be sequenced 
was insulin, by Frederick Sanger, who won the Nobel Prize for this achievement in 1958. The first protein structures 
to be solved were hemoglobin and myoglobin, by Max Perutz and Sir John Cowdery Kendrew, respectively, in 
1958. The three-dimensional structures of both proteins were first determined by x-ray diffraction analysis; 

Perutz and Kendrew shared the 1962 Nobel Prize in Chemistry for these discoveries. Proteins may be purified from 
other cellular components using a variety of techniques such as ultracentrifugation, precipitation, electrophoresis, 
and chromatography; the advent of genetic engineering has made possible a number of methods to facilitate 
purification. Methods commonly used to study protein structure and function include immunohistochemistry, 
site-directed mutagenesis, and mass spectrometry. 



Biochemistry 

Most proteins are linear polymers built from 
series of up to 20 different L-a-amino acids. 
All amino acids possess common structural 
features, including an a-carbon to which an 
amino group, a carboxyl group, and a 



w 



£tt^\A 




£tt^\A 



/ \ 

Resonance structures of the peptide bond that links individual amino acids to form 
a protein polymer. 



Proteins 



146 



variable side chain are bonded. Only proline differs from this basic structure as it contains an unusual ring to the 

rsi 
N-end amine group, which forces the CO— NH amide moiety into a fixed conformation. The side chains of the 

standard amino acids, detailed in the list of standard amino acids, have a great variety of chemical structures and 

properties; it is the combined effect of all of the amino acid side chains in a protein that ultimately determines its 

three-dimensional structure and its chemical reactivity 



[9] 



o 




R 



V 



n 



Chemical structure of the peptide bond (left) and a peptide bond between leucine and threonine (right). 

The amino acids in a polypeptide chain are linked by peptide bonds. Once linked in the protein chain, an individual 
amino acid is called a residue, and the linked series of carbon, nitrogen, and oxygen atoms are known as the main 
chain or protein backbone. The peptide bond has two resonance forms that contribute some double-bond 
character and inhibit rotation around its axis, so that the carbons are roughly coplanar. The other two dihedral angles 
in the peptide bond determine the local shape assumed by the protein backbone. The end of the protein with a free 
carboxyl group is known as the C-terminus or carboxy terminus, whereas the end with a free amino group is known 
as the N-terminus or amino terminus. 

The words protein, polypeptide, and peptide are a little ambiguous and can overlap in meaning. Protein is generally 
used to refer to the complete biological molecule in a stable conformation, whereas peptide is generally reserved for 
a short amino acid oligomers often lacking a stable three-dimensional structure. However, the boundary between the 
two is not well defined and usually lies near 20—30 residues. Polypeptide can refer to any single linear chain of 
amino acids, usually regardless of length, but often implies an absence of a defined conformation. 



Synthesis 



GTGCATCTGACTCCTGAGGAGAAG 
CACGTAGACTGAGGACTCCTCTTC 

I 

GUGCAUCUGACUCCUGAGGAGAAG 

TrTTTTTT 



v H L 



E E K 



. DNA 

(transcription) 
. RNA 

(translation) 

protein 



The DNA sequence of a gene encodes the amino acid sequence of a protein. 



Proteins are assembled from amino acids 
using information encoded in genes. Each 
protein has its own unique amino acid 
sequence that is specified by the nucleotide 
sequence of the gene encoding this protein. 
The genetic code is a set of three-nucleotide 
sets called codons and each three-nucleotide 
combination designates an amino acid, for 
example AUG (adenine-uracil-guanine) is 
the code for methionine. Because DNA 
contains four nucleotides, the total number of possible codons is 64; hence, there is some redundancy in the genetic 

ri3i 

code, with some amino acids specified by more than one codon. Genes encoded in DNA are first transcribed into 
pre-messenger RNA (mRNA) by proteins such as RNA polymerase. Most organisms then process the pre-mRNA 
(also known as a primary transcript) using various forms of post-transcriptional modification to form the mature 
mRNA, which is then used as a template for protein synthesis by the ribosome. In prokaryotes the mRNA may either 
be used as soon as it is produced, or be bound by a ribosome after having moved away from the nucleoid. In contrast, 
eukaryotes make mRNA in the cell nucleus and then translocate it across the nuclear membrane into the cytoplasm, 
where protein synthesis then takes place. The rate of protein synthesis is higher in prokaryotes than eukaryotes and 
can reach up to 20 amino acids per second. 



Proteins 



147 



The process of synthesizing a protein from an mRNA template is known as translation. The mRNA is loaded onto 
the ribosome and is read three nucleotides at a time by matching each codon to its base pairing anticodon located on 
a transfer RNA molecule, which carries the amino acid corresponding to the codon it recognizes. The enzyme 
aminoacyl tRNA synthetase "charges" the tRNA molecules with the correct amino acids. The growing polypeptide is 

ri3i 

often termed the nascent chain. Proteins are always biosynthesized from N-terminus to C-terminus. 

The size of a synthesized protein can be measured by the number of amino acids it contains and by its total 

molecular mass, which is normally reported in units of daltons (synonymous with atomic mass units), or the 

ri2i 
derivative unit kilodalton (kDa). Yeast proteins are on average 466 amino acids long and 53 kDa in mass. The 

largest known proteins are the titins, a component of the muscle sarcomere, with a molecular mass of almost 3,000 



kDa and a total length of almost 27,000 amino acids 



[15] 



Chemical synthesis 

Short proteins can also be synthesized chemically by a family of methods known as peptide synthesis, which rely on 
organic synthesis techniques such as chemical ligation to produce peptides in high yield. Chemical synthesis 
allows for the introduction of non-natural amino acids into polypeptide chains, such as attachment of fluorescent 

ri7i 

probes to amino acid side chains. These methods are useful in laboratory biochemistry and cell biology, though 
generally not for commercial applications. Chemical synthesis is inefficient for polypeptides longer than about 300 

amino acids, and the synthesized proteins may not readily assume their native tertiary structure. Most chemical 

n ri 
synthesis methods proceed from C-terminus to N-terminus, opposite the biological reaction. 




Structure of proteins 

Most proteins fold into unique 
3 -dimensional structures. The shape 
into which a protein naturally folds is 
known as its native conformation. 
Although many proteins can fold 
unassisted, simply through the 
chemical properties of their amino 
acids, others require the aid of 
molecular chaperones to fold into their 
native states. Biochemists often 

refer to four distinct aspects of a 
protein's structure: 

• Primary structure: the amino acid 
sequence. 

• Secondary structure: regularly repeating local structures stabilized by hydrogen bonds. The most common 
examples are the alpha helix, beta sheet and turns. Because secondary structures are local, many regions of 
different secondary structure can be present in the same protein molecule. 

• Tertiary structure: the overall shape of a single protein molecule; the spatial relationship of the secondary 
structures to one another. Tertiary structure is generally stabilized by nonlocal interactions, most commonly the 
formation of a hydrophobic core, but also through salt bridges, hydrogen bonds, disulfide bonds, and even 
post-translational modifications. The term "tertiary structure" is often used as synonymous with the term fold. The 
Tertiary structure is what controls the basic function of the protein. 

• Quaternary structure: the structure formed by several protein molecules (polypeptide chains), usually called 
protein subunits in this context, which function as a single protein complex. 



Three possible representations of the three-dimensional structure of the protein triose 

phosphate isomerase. Left: all-atom representation colored by atom type. Middle: 

Simplified representation illustrating the backbone conformation, colored by secondary 

structure. Right: Solvent-accessible surface representation colored by residue type (acidic 

residues red, basic residues blue, polar residues green, nonpolar residues white). 



Proteins 



148 



[22] 



Proteins are not entirely rigid molecules. In addition to these levels of structure, proteins may shift between several 

related structures while they perform their functions. In the context of these functional rearrangements, these tertiary 

or quaternary structures are usually referred to as "conformations", and transitions between them are called 

conformational changes. Such changes are often induced by the binding of a substrate molecule to an enzyme's 

active site, or the physical region of the protein that participates in chemical catalysis. In solution proteins also 

p 
undergo variation in structure through thermal vibration and the collision with other molecules. 

Proteins can be informally divided into 
three main classes, which correlate 
with typical tertiary structures: 
globular proteins, fibrous proteins, and 
membrane proteins. Almost all 
globular proteins are soluble and many 
are enzymes. Fibrous proteins are often 
structural, such as collagen, the major 
component of connective tissue, or 
keratin, the protein component of hair 
and nails. Membrane proteins often serve as receptors or provide channels for polar or charged molecules to pass 




Molecular surface of several proteins showing their comparative sizes. From left to right 

are: immunoglobulin G (IgG, an antibody), hemoglobin, insulin (a hormone), adenylate 

kinase (an enzyme), and glutamine synthetase (an enzyme). 



through the cell membrane 



[23] 



A special case of intramolecular hydrogen bonds within proteins, poorly shielded from water attack and hence 



promoting their own dehydration, are called dehydrons 



[24] 



Structure determination 

Discovering the tertiary structure of a protein, or the quaternary structure of its complexes, can provide important 

clues about how the protein performs its function. Common experimental methods of structure determination include 

X-ray crystallography and NMR spectroscopy, both of which can produce information at atomic resolution. Dual 

polarisation interferometry is a quantitative analytical method for measuring the overall protein conformation and 

conformational changes due to interactions or other stimulus. Circular dichroism is another laboratory technique for 

determining internal beta sheet/ helical composition of proteins. Cryoelectron microscopy is used to produce 

[251 
lower-resolution structural information about very large protein complexes, including assembled viruses; a 

variant known as electron crystallography can also produce high-resolution information in some cases , especially 

for two-dimensional crystals of membrane proteins. Solved structures are usually deposited in the Protein Data 

Bank (PDB), a freely available resource from which structural data about thousands of proteins can be obtained in 



the form of Cartesian coordinates for each atom in the protein 



[27] 



Many more gene sequences are known than protein structures. Further, the set of solved structures is biased toward 
proteins that can be easily subjected to the conditions required in X-ray crystallography, one of the major structure 
determination methods. In particular, globular proteins are comparatively easy to crystallize in preparation for X-ray 

["981 

crystallography. Membrane proteins, by contrast, are difficult to crystallize and are underrepresented in the PDB. 
Structural genomics initiatives have attempted to remedy these deficiencies by systematically solving representative 
structures of major fold classes. Protein structure prediction methods attempt to provide a means of generating a 
plausible structure for proteins whose structures have not been experimentally determined. 



Proteins 



149 



Cellular functions 

Proteins are the chief actors within the cell, said to be carrying out the duties specified by the information encoded in 

ri2i 
genes. With the exception of certain types of RNA, most other biological molecules are relatively inert elements 

upon which proteins act. Proteins make up half the dry weight of an Escherichia coli cell, whereas other 



macromolecules such as DNA and RNA make up only 3% and 20%, respectively 
in a particular cell or cell type is known as its proteome. 

The chief characteristic of proteins that 
also allows their diverse set of 
functions is their ability to bind other 
molecules specifically and tightly. The 
region of the protein responsible for 
binding another molecule is known as 
the binding site and is often a 
depression or "pocket" on the 
molecular surface. This binding ability 
is mediated by the tertiary structure of 
the protein, which defines the binding 
site pocket, and by the chemical 
properties of the surrounding amino 
acids' side chains. Protein binding can 
be extraordinarily tight and specific; 
for example, the ribonuclease inhibitor 
protein binds to human angiogenin 



[29] 



The set of proteins expressed 




The enzyme hexokinase is shown as a simple ball-and-stick molecular model. To scale in 
the top right-hand corner are two of its substrates, ATP and glucose. 



-15 



with a sub-femtomolar dissociation constant (<10~ M) but does not bind at all to its amphibian homolog onconase 
(>1 M). Extremely minor chemical changes such as the addition of a single methyl group to a binding partner can 
sometimes suffice to nearly eliminate binding; for example, the aminoacyl tRNA synthetase specific to the amino 



acid valine discriminates against the very similar side chain of the amino acid isoleucine 



[30] 



Proteins can bind to other proteins as well as to small-molecule substrates. When proteins bind specifically to other 
copies of the same molecule, they can oligomerize to form fibrils; this process occurs often in structural proteins that 
consist of globular monomers that self-associate to form rigid fibers. Protein— protein interactions also regulate 
enzymatic activity, control progression through the cell cycle, and allow the assembly of large protein complexes 
that carry out many closely related reactions with a common biological function. Proteins can also bind to, or even 
be integrated into, cell membranes. The ability of binding partners to induce conformational changes in proteins 

[31] 

allows the construction of enormously complex signaling networks. Importantly, as interactions between proteins 
are reversible, and depend heavily on the availability of different groups of partner proteins to form aggregates that 
are capable to carry out discrete sets of function, study of the interactions between specific proteins is a key to 
understand important aspects of cellular function, and ultimately the properties that distinguish particular cell 

[32] [33] 

types 



Enzymes 

The best-known role of proteins in the cell is as enzymes, which catalyze chemical reactions. Enzymes are usually 
highly specific and accelerate only one or a few chemical reactions. Enzymes carry out most of the reactions 
involved in metabolism, as well as manipulating DNA in processes such as DNA replication, DNA repair, and 

transcription. Some enzymes act on other proteins to add or remove chemical groups in a process known as 

[34] 
post-translational modification. About 4,000 reactions are known to be catalyzed by enzymes. The rate 

17 

acceleration conferred by enzymatic catalysis is often enormous — as much as 10 -fold increase in rate over the 



Proteins 



150 



uncatalyzed reaction in the case of orotate decarboxylase (78 million years without the enzyme, 18 milliseconds with 
the enzyme). 

The molecules bound and acted upon by enzymes are called substrates. Although enzymes can consist of hundreds 
of amino acids, it is usually only a small fraction of the residues that come in contact with the substrate, and an even 



smaller fraction — 3 to 4 residues on average — that are directly involved in catalysis 
that binds the substrate and contains the catalytic residues is known as the active site. 



[36] 



The region of the enzyme 



Cell signaling and ligand binding 

Many proteins are involved in the process of cell signaling and signal 
transduction. Some proteins, such as insulin, are extracellular proteins 
that transmit a signal from the cell in which they were synthesized to 
other cells in distant tissues. Others are membrane proteins that act as 
receptors whose main function is to bind a signaling molecule and 
induce a biochemical response in the cell. Many receptors have a 
binding site exposed on the cell surface and an effector domain within 
the cell, which may have enzymatic activity or may undergo a 
conformational change detected by other proteins within the cell 



[37] 



Antibodies are protein components of adaptive immune system whose 
main function is to bind antigens, or foreign substances in the body, 
and target them for destruction. Antibodies can be secreted into the 
extracellular environment or anchored in the membranes of specialized 
B cells known as plasma cells. Whereas enzymes are limited in their 
binding affinity for their substrates by the necessity of conducting their 
reaction, antibodies have no such constraints. An antibody's binding 
affinity to its target is extraordinarily high 



[38] 




Ribbon diagram of a mouse antibody against 
cholera that binds a carbohydrate antigen 



Many ligand transport proteins bind particular small biomolecules and 

transport them to other locations in the body of a multicellular 

organism. These proteins must have a high binding affinity when their ligand is present in high concentrations, but 

must also release the ligand when it is present at low concentrations in the target tissues. The canonical example of a 

ligand-binding protein is haemoglobin, which transports oxygen from the lungs to other organs and tissues in all 

[39] 
vertebrates and has close homologs in every biological kingdom. Lectins are sugar-binding proteins which are 

highly specific for their sugar moieties. Lectins typically play a role in biological recognition phenomena involving 

cells and proteins. Receptors and hormones are highly specific binding proteins. 

Transmembrane proteins can also serve as ligand transport proteins that alter the permeability of the cell membrane 
to small molecules and ions. The membrane alone has a hydrophobic core through which polar or charged molecules 
cannot diffuse. Membrane proteins contain internal channels that allow such molecules to enter and exit the cell. 
Many ion channel proteins are specialized to select for only a particular ion; for example, potassium and sodium 



channels often discriminate for only one of the two ions 



[41] 



Structural proteins 

Structural proteins confer stiffness and rigidity to otherwise-fluid biological components. Most structural proteins are 
fibrous proteins; for example, actin and tubulin are globular and soluble as monomers, but polymerize to form long, 
stiff fibers that comprise the cytoskeleton, which allows the cell to maintain its shape and size. Collagen and elastin 
are critical components of connective tissue such as cartilage, and keratin is found in hard or filamentous structures 



such as hair, nails, feathers, hooves, and some animal shells 



[42] 



Proteins 151 

Other proteins that serve structural functions are motor proteins such as myosin, kinesin, and dynein, which are 
capable of generating mechanical forces. These proteins are crucial for cellular motility of single celled organisms 
and the sperm of many multicellular organisms which reproduce sexually. They also generate the forces exerted by 
contracting muscles. 

Methods of study 

As some of the most commonly studied biological molecules, the activities and structures of proteins are examined 
both in vitro and in vivo. In vitro studies of purified proteins in controlled environments are useful for learning how a 
protein carries out its function: for example, enzyme kinetics studies explore the chemical mechanism of an enzyme's 
catalytic activity and its relative affinity for various possible substrate molecules. By contrast, in vivo experiments on 
proteins' activities within cells or even within whole organisms can provide complementary information about where 
a protein functions and how it is regulated. 

Protein purification 

In order to perform in vitro analysis, a protein must be purified away from other cellular components. This process 
usually begins with cell lysis, in which a cell's membrane is disrupted and its internal contents released into a 
solution known as a crude lysate. The resulting mixture can be purified using ultracentrifugation, which fractionates 
the various cellular components into fractions containing soluble proteins; membrane lipids and proteins; cellular 
organelles, and nucleic acids. Precipitation by a method known as salting out can concentrate the proteins from this 

lysate. Various types of chromatography are then used to isolate the protein or proteins of interest based on 

T441 
properties such as molecular weight, net charge and binding affinity. The level of purification can be monitored 

using various types of gel electrophoresis if the desired protein's molecular weight and isoelectric point are known, 

by spectroscopy if the protein has distinguishable spectroscopic features, or by enzyme assays if the protein has 

[451 
enzymatic activity. Additionally, proteins can be isolated according their charge using electrofocusing. 

For natural proteins, a series of purification steps may be necessary to obtain protein sufficiently pure for laboratory 
applications. To simplify this process, genetic engineering is often used to add chemical features to proteins that 
make them easier to purify without affecting their structure or activity. Here, a "tag" consisting of a specific amino 
acid sequence, often a series of histidine residues (a "His-tag"), is attached to one terminus of the protein. As a result, 
when the lysate is passed over a chromatography column containing nickel, the histidine residues ligate the nickel 
and attach to the column while the untagged components of the lysate pass unimpeded. A number of different tags 
have been developed to help researchers purify specific proteins from complex mixtures. 



Proteins 



152 



Cellular localization 

The study of proteins in vivo is often concerned 
with the synthesis and localization of the protein 
within the cell. Although many intracellular 
proteins are synthesized in the cytoplasm and 
membrane-bound or secreted proteins in the 
endoplasmic reticulum, the specifics of how 
proteins are targeted to specific organelles or 
cellular structures is often unclear. A useful 
technique for assessing cellular localization uses 
genetic engineering to express in a cell a fusion 
protein or chimera consisting of the natural 

protein of interest linked to a "reporter" such as 

1471 
green fluorescent protein (GFP). The fused 

protein's position within the cell can be cleanly 

and efficiently visualized using microscopy, 

as shown in the figure opposite. 

Other methods for elucidating the cellular 

location of proteins requires the use of known 

compartmental markers for regions such as the 

ER, the Golgi, lysosomes/vacuoles, 

mitochondria, chloroplasts, plasma membrane, 

etc. With the use of fluorescently-tagged 

versions of these markers or of antibodies to 

known markers, it becomes much simpler to 

identify the localization of a protein of interest. 

For example, indirect immunofluorescence will allow for fluorescence colocalization and demonstration of location. 

Fluorescent dyes are used to label cellular compartments for a similar purpose. 

Other possibilities exist, as well. For example, immunohistochemistry usually utilizes an antibody to one or more 
proteins of interest that are conjugated to enzymes yielding either luminescent or chromogenic signals that can be 
compared between samples, allowing for localization information. Another applicable technique is cofractionation in 
sucrose (or other material) gradients using isopycnic centrifugation. While this technique does not prove 
colocalization of a compartment of known density and the protein of interest, it does increase the likelihood, and is 
more amenable to large-scale studies. 

Finally, the gold-standard method of cellular localization is immunoelectron microscopy. This technique also uses an 
antibody to the protein of interest, along with classical electron microscopy techniques. The sample is prepared for 
normal electron microscopic examination, and then treated with an antibody to the protein of interest that is 
conjugated to an extremely electro-dense material, usually gold. This allows for the localization of both 
ultrastructural details as well as the protein of interest. 

Through another genetic engineering application known as site-directed mutagenesis, researchers can alter the 
protein sequence and hence its structure, cellular localization, and susceptibility to regulation. This technique even 

T521 

allows the incorporation of unnatural amino acids into proteins, using modified tRNAs, and may allow the 

[531 
rational design of new proteins with novel properties. 




wtth friendlv oermission of Jeremv Simoson and Rainer PeoDerkok 
Proteins in different cellular compartments and structures tagged with green 
fluorescent protein) (here, white). 



Proteins 153 

Proteomics and bioinformatics 

The total complement of proteins present at a time in a cell or cell type is known as its proteome, and the study of 
such large-scale data sets defines the field of proteomics, named by analogy to the related field of genomics. Key 
experimental techniques in proteomics include 2D electrophoresis, which allows the separation of a large number 
of proteins, mass spectrometry, which allows rapid high-throughput identification of proteins and sequencing of 
peptides (most often after in-gel digestion), protein microarrays, which allow the detection of the relative levels 
of a large number of proteins present in a cell, and two-hybrid screening, which allows the systematic exploration of 

T571 

protein— protein interactions. The total complement of biologically possible such interactions is known as the 

reel 

interactome. A systematic attempt to determine the structures of proteins representing every possible fold is 
known as structural genomics. 

The large amount of genomic and proteomic data available for a variety of organisms, including the human genome, 
allows researchers to efficiently identify homologous proteins in distantly related organisms by sequence alignment. 
Sequence profiling tools can perform more specific sequence manipulations such as restriction enzyme maps, open 
reading frame analyses for nucleotide sequences, and secondary structure prediction. From this data phylogenetic 
trees can be constructed and evolutionary hypotheses developed using special software like ClustalW regarding the 
ancestry of modern organisms and the genes they express. The field of bioinformatics seeks to assemble, annotate, 
and analyze genomic and proteomic data, applying computational techniques to biological problems such as gene 
finding and cladistics. 

Structure prediction and simulation 

Complementary to the field of structural genomics, protein structure prediction seeks to develop efficient ways to 
provide plausible models for proteins whose structures have not yet been determined experimentally . The most 
successful type of structure prediction, known as homology modeling, relies on the existence of a "template" 
structure with sequence similarity to the protein being modeled; structural genomics' goal is to provide sufficient 
representation in solved structures to model most of those that remain. Although producing accurate models 
remains a challenge when only distantly related template structures are available, it has been suggested that sequence 
alignment is the bottleneck in this process, as quite accurate models can be produced if a "perfect" sequence 
alignment is known. Many structure prediction methods have served to inform the emerging field of protein 
engineering, in which novel protein folds have already been designed. A more complex computational problem is 
the prediction of intermolecular interactions, such as in molecular docking and protein— protein interaction 
prediction. 

The processes of protein folding and binding can be simulated using such technique as molecular mechanics, in 
particular, molecular dynamics and Monte Carlo, which increasingly take advantage of parallel and distributed 
computing (Folding@Home project ; molecular modeling on GPU). The folding of small alpha-helical protein 
domains such as the villin headpiece and the HIV accessory protein have been successfully simulated in silico, 
and hybrid methods that combine standard molecular dynamics with quantum mechanics calculations have allowed 
exploration of the electronic states of rhodopsins. 

Nutrition 

Most microorganisms and plants can biosynthesize all 20 standard amino acids, while animals (including humans) 

[291 
must obtain some of the amino acids from the diet. The amino acids that an organism cannot synthesize on its 

own are referred to as essential amino acids. Key enzymes that synthesize certain amino acids are not present in 

animals — such as aspartokinase, which catalyzes the first step in the synthesis of lysine, methionine, and threonine 

from aspartate. If amino acids are present in the environment, microorganisms can conserve energy by taking up the 

amino acids from their surroundings and downregulating their biosynthetic pathways. 



Proteins 154 

In animals, amino acids are obtained through the consumption of foods containing protein. Ingested proteins are then 
broken down into amino acids through digestion, which typically involves denaturation of the protein through 
exposure to acid and hydrolysis by enzymes called proteases. Some ingested amino acids are used for protein 
biosynthesis, while others are converted to glucose through gluconeogenesis, or fed into the citric acid cycle. This 
use of protein as a fuel is particularly important under starvation conditions as it allows the body's own proteins to be 
used to support life, particularly those found in muscle. Amino acids are also an important dietary source of 
nitrogen. 

History and etymology 

Proteins were recognized as a distinct class of biological molecules in the eighteenth century by Antoine Fourcroy 
and others, distinguished by the molecules' ability to coagulate or flocculate under treatments with heat or acid. 
Noted examples at the time included albumin from egg whites, blood serum albumin, fibrin, and wheat gluten. Dutch 
chemist Gerhardus Johannes Mulder carried out elemental analysis of common proteins and found that nearly all 
proteins had the same empirical formula, C,„„H,„N,-„0,,,„P,S,. He came to the erroneous conclusion that they 

r r 400 620 100 120 1 1 J 

might be composed of a single type of (very large) molecule. The term "protein" to describe these molecules was 
proposed in 1838 by Mulder's associate Jons Jakob Berzelius; protein is derived from the Greek word xpmxeloc, 

T711 T721 

(proteios), meaning "primary" , "in the lead", or "standing in front". Mulder went on to identify the products of 
protein degradation such as the amino acid leucine for which he found a (nearly correct) molecular weight of 131 
Da. [70] 

The difficulty in purifying proteins in large quantities made them very difficult for early protein biochemists to 
study. Hence, early studies focused on proteins that could be purified in large quantities, e.g., those of blood, egg 
white, various toxins, and digestive/metabolic enzymes obtained from slaughterhouses. In the 1950s, the Armour 
Hot Dog Co. purified 1 kg of pure bovine pancreatic ribonuclease A and made it freely available to scientists; this 
gesture helped ribonuclease A become a major target for biochemical study for the following decades. 

Linus Pauling is credited with the successful prediction of regular protein secondary structures based on hydrogen 

T731 T741 

bonding, an idea first put forth by William Astbury in 1933. Later work by Walter Kauzmann on denaturation, 

based partly on previous studies by Kaj Linderstr0m-Lang, contributed an understanding of protein folding 

and structure mediated by hydrophobic interactions. In 1949 Fred Sanger correctly determined the amino acid 

sequence of insulin, thus conclusively demonstrating that proteins consisted of linear polymers of amino acids rather 

T771 
than branched chains, colloids, or cyclols. The first atomic-resolution structures of proteins were solved by X-ray 

crystallography in the 1960s and by NMR in the 1980s. As of 2009, the Protein Data Bank has over 55,000 

T7R1 

atomic-resolution structures of proteins. In more recent times, cryo-electron microscopy of large macromolecular 
assemblies and computational protein structure prediction of small protein domains are two methods 
approaching atomic resolution. 

See also 

Expression cloning 

Intein 

List of proteins 

List of recombinant proteins 

Prion 

Protein design 

Protein dynamics 

Protein structure prediction software 

Proteopathy 

Proteopedia 



Proteins 155 

• Cdx protein family 

References 

• Branden C, Tooze J. (1999). Introduction to Protein Structure. New York: Garland Pub. ISBN 0-8153-2305-0. 

• Murray RF, Harper HW, Granner DK, Mayes PA, Rodwell VW. (2006). Harper's Illustrated Biochemistry . New 
York: Lange Medical Books/McGraw-Hill. ISBN 0-07-146197-3. 

• Van Holde KE, Mathews CK. (1996). Biochemistry . Menlo Park, Calif: Benjamin/Cummings Pub. Co., Inc. 
ISBN 0-8053-3931-0. 

• Jorg von Hagen, VCH-Wiley 2008 Proteomics Sample Preparation. ISBN 978-3-527-31796-7 

External links 

[81 ] 

• Protein Songs (Stuart Mitchell — DNA Music Project) , 'When a "tape" of mRNA passes through the "playing 
head" of a ribosome, the "notes" produced are amino acids and the pieces of music they make up are proteins.' 

Databases and projects 

rs2i 

• Comparative Toxicogenomics Database curates protein— chemical interactions, as well as 

gene/protein— disease relationships and chemical-disease relationships. 

• Bioinformatic Harvester A Meta search engine (29 databases) for gene and protein information. 

• The Protein Databank (see also PDB Molecule of the Month , presenting short accounts on selected 
proteins from the PDB) 

• Proteopedia — Life in 3D : rotatable, zoomable 3D model with wiki annotations for every known protein 



molecular structure. 

al Prote 

[88] 



rs7i 
• UniProt the Universal Protein Resource 



• The Protein Naming Utility 

• Human Protein Atlas 

• NCBI Entrez Protein database 

• NCBI Protein Structure database [91] 

[92] 

• Human Protein Reference Database 

• Human Proteinpedia 

[94] 

• Folding© Home (Stanford University) 



Tutorials and educational websites 



[95] 

• "An Introduction to Proteins" from HOPES (Huntington's Disease Outreach Project for Education at Stanford) 

• Proteins: Biogenesis to Degradation — The Virtual Library of Biochemistry and Cell Biology 

References 

[1] http://en.wikipedia.org/w/index.php?title=Wikipedia_talk:WikiProject_Molecular_and_Cellular_Biology&action=edit&section=new 

[2] http://en.wikipedia.org/w/index.php?title=Template:MolBioGeneExp&action=edit 

[3] Ridley, M. (2006). Genome. New York, NY: Harper Perennial. ISBN 0-06-019497-9 

[4] Maton A, Hopkins J, McLaughlin CW, Johnson S, Warner MQ, LaHart D, Wright JD. (1993). Human Biology and Health. Englewood Cliffs, 

Michigan, USA: Prentice Hall. ISBN 0-13-981176-1. OCLC 32308337. 
[5] Sumner, JB. (1926). "The isolation and crystallization of the enzyme urease. Preliminary paper" (http://www.jbc.Org/cgi/reprint/69/2/ 

435.pdf?ijkey=028d5e540dab50accbf86e01be08db51ef49008f). Journal of Biological Chemistry 69: 435-41. . 
[6] Muirhead H, Perutz M. (1963). "Structure of hemoglobin. A three-dimensional fourier synthesis of reduced human hemoglobin at 5.5 A 

resolution". Nature 199 (4894): 633-38. doi:10.1038/199633a0. PMID 14074546. 
[7] Kendrew J, Bodo G, Dintzis H, Parrish R, Wyckoff H, Phillips D. (1958). "A three-dimensional model of the myoglobin molecule obtained 

by x-ray analysis". Nature 181 (4610): 662-66. doi:10.1038/181662a0. PMID 13517261. 
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Proteins 156 

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[81] http 

[82] http 

[83] http 

[84] http 

[85] http 

[86] http 

[87] http 

[88] http 

[89] http 

[90] http 

[91] http 

[92] http 

[93] http 

[94] http 

[95] http 

[96] http 



//www. tjmitchell.com/stuart/dna.html 

//ctd. mdibl.org/ 

//harvester.fzk.de 

//www. rcsb.org 

//www. rcsb.org/pdb/static. do ?p=education_discussion/molecule_of_the_month/index. html 

//www. proteopedia.org 

//www. expasy.uniprot.org 

//www.jcvi.org/pn-utility 

// w w w. pro teinatlas . org 

//www. ncbi.nlm. nih. go v/sites/entrez?db=protein 

//www. ncbi.nlm. nih. go v/sites/entrez?db=structure 

//www. hprd.org/ 

//www. humanproteinpedia.org/ 

//folding, stanford.edu/ 

//hopes. stanford.edu/basics/proteins/pO. html 

//www. biochemweb.org/proteins.shtml 



Protein structure 



159 



Protein structure 



Proteins are an important class of biological macromolecules present in all biological organisms, made up of such 
elements as carbon, hydrogen, nitrogen, oxygen, and sulphur. All proteins are polymers of amino acids. According to 
their physical size, proteins are nanoparticles (definition: 1-100 nm). The polymers, also known as polypeptides, 
consist of a sequence of 20 different L-a-amino acids, also referred to as residues. For chains under 40 residues the 
term peptide is frequently used instead of protein. To be able to perform their biological function, proteins fold into 
one or more specific spatial conformations, driven by a number of noncovalent interactions such as hydrogen 
bonding, ionic interactions, Van Der Waals forces and hydrophobic packing. To understand the functions of proteins 
at a molecular level, it is often necessary to determine their three dimensional structure. This is the topic of the 
scientific field of structural biology, that employs techniques such as X-ray crystallography, NMR spectroscopy, and 
Dual Polarisation Interferometry to determine the structure of proteins. 

A number of residues is necessary to perform a particular biochemical function, and around 40-50 residues appears 
to be the lower limit for a functional domain size. Protein sizes range from this lower limit to several thousand 
residues in multi-functional or structural proteins. However, the current estimate for the average protein length is 
around 300 residues. Very large aggregates can be formed from protein subunits, for example many thousand actin 
molecules assemble into a microfilament. 



Levels of protein structure 



Primary protein emicnire 

is sequence of s chain oT amino asids 



Amino Acids 



Alpha helix 



Biochemistry refers to four distinct aspects of a 
protein's structure: 

Primary structure 

the amino acid sequence of the peptide chains. 

Secondary structure 

highly regular sub-structures (alpha helix and 
strands of beta pleated sheet), which are locally 
defined, meaning that there can be many 
different secondary motifs present in one single 
protein molecule. 

Tertiary structure 

three-dimensional structure of a single protein 
molecule; a spatial arrangement of the secondary 
structures. It also describes the completely folded 
and compacted polypeptide chain. 

Quaternary structure 

complex of several protein molecules or 
polypeptide chains, usually called protein 
subunits in this context, which function as part of 
the larger assembly or protein complex. 

In addition to these levels of structure, a protein may 
shift between several similar structures in performing its biological function. This process is also reversible. In the 
context of these functional rearrangements, these tertiary or quaternary structures are usually referred to as chemical 
conformation, and transitions between them are called conformational changes. 




Secondary protein auijclijre 

occurs, when ma sequence of amino acirjs 
are linked by hydrogen tends 



Pleated sheet 

Tertiary protein structure 

occursiwhsn certain attractions are pre&em 
between alpha helcsa end pleated Shasta. 



°- Alpha heJix 



Quaternary protein structure 

ib a protein consisting of more man one 
amino end chain 



Protein structure, from primary to quaternary structure. 



Protein structure 160 

The primary structure is held together by covalent or peptide bonds, which are made during the process of protein 
biosynthesis or translation. These peptide bonds provide rigidity to the protein. The two ends of the amino acid chain 
are referred to as the C-terminal end or carboxyl terminus (C-terminus) and the N-terminal end or amino terminus 
(N-terminus) based on the nature of the free group on each extremity. 

The various types of secondary structure are defined by their patterns of hydrogen bonds between the main-chain 
peptide groups. However, these hydrogen bonds are generally not stable by themselves, since the water-amide 
hydrogen bond is generally more favorable than the amide-amide hydrogen bond. Thus, secondary structure is stable 
only when the local concentration of water is sufficiently low, e.g., in the molten globule or fully folded states. 

Similarly, the formation of molten globules and tertiary structure is driven mainly by structurally non-specific 
interactions, such as the rough propensities of the amino acids and hydrophobic interactions. However, the tertiary 
structure is fixed only when the parts of a protein domain are locked into place by structurally specific interactions, 
such as ionic interactions (salt bridges), hydrogen bonds, and the tight packing of side chains. The tertiary structure 
of extracellular proteins can also be stabilized by disulfide bonds, which reduce the entropy of the unfolded state; 
disulfide bonds are extremely rare in cytosolic proteins, since the cytosol is generally a reducing environment. 

Primary structure 

The sequence of the different amino acids is called the primary structure of the peptide or protein. Counting of 
residues always starts at the N-terminal end (NH -group), which is the end where the amino group is involved in a 
peptide bond. The primary structure of a protein is determined by the gene corresponding to the protein. A specific 
sequence of nucleotides in DNA is transcribed into mRNA, which is read by the ribosome in a process called 
translation. The sequence of a protein is unique to that protein, and defines the structure and function of the protein. 
The sequence of a protein can be determined by methods such as Edman degradation or tandem mass spectrometry. 
Often however, it is read directly from the sequence of the gene using the genetic code. Post-translational 
modifications such as disulfide formation, phosphorylations and glycosylations are usually also considered a part of 
the primary structure, and cannot be read from the gene. 

Secondary structure 




Protein structure 161 




Left: Ca atom trace. Right: Secondary structure cartoon ("ribbon") 

By building models of peptides using known information about bond lengths and angles, the first elements of 
secondary structure, the alpha helix and the beta sheet, were suggested in 1951 by Linus Pauling and coworkers. 
Each of these two secondary structure elements have a regular geometry, meaning they are constrained to specific 
values of the dihedral angles t|> and ep. Thus they can be found in a specific region of the Ramachandran plot. Both 
the alpha helix and the beta-sheet represent a way of saturating all the hydrogen bond donors and acceptors in the 
peptide backbone. These secondary structure elements only depend on properties of the polypeptide main chain, 
explaining why they occur in all proteins. The part of the protein that is not in a regular secondary structure is said to 
be a "non-regular structure" (not to be mixed with random coil, an unfolded polypeptide chain lacking any fixed 
three-dimensional structure). Some more representations of the same helix are shown at right. 

Supersecondary structure 

The elements of secondary structure are usually folded into a compact shape using a variety of loops and turns. 
Secondary structures are bonded by hydrogen bond to form supersecondary structures like Greek key. See 
Supersecondary structure for a detailed example. It is also suggested by many scientists that th secondary structure 
consists only of the amino acid sequence. 

Tertiary structure 

The elements of secondary structure are usually folded into a compact shape using a variety of loops and turns. The 
formation of tertiary structure is usually driven by the burial of hydrophobic residues, but other interactions such as 
hydrogen bonding, ionic interactions and disulfide bonds can also stabilize the tertiary structure. The tertiary 
structure encompasses all the noncovalent interactions that are not considered secondary structure, and is what 
defines the overall fold of the protein, and is usually indispensable for the function of the protein. 

Quaternary structure 

The quaternary structure is the interaction between several chains of peptide bonds. The individual chains are called 
subunits. The individual subunits are usually not covalently connected, but might be connected by a disulfide bond. 
Not all proteins have quaternary structure, since they might be functional as monomers. The quaternary structure is 
stabilized by the same range of interactions as the tertiary structure. Complexes of two or more polypeptides (i.e. 
multiple subunits) are called multimers. Specifically it would be called a dimer if it contains two subunits, a trimer if 
it contains three subunits, and a tetramer if it contains four subunits. The subunits are usually related to one another 
by symmetry axes, such as a 2-fold axis in a dimer. Multimers made up of identical subunits may be referred to with 
a prefix of "homo-" (e.g. a homotetramer) and those made up of different subunits may be referred to with a prefix of 
"hetero-" (e.g. a heterotetramer, such as the two alpha and two beta chains of hemoglobin). 



Protein structure 



162 



Structure of the amino acids 

An oc-amino acid consists of a part that is present in all 
the amino acid types, and a side chain that is unique to 
each type of residue. The C atom is bound to 4 

a 

different atoms: a hydrogen atom (the H is omitted in 
the diagram), an amino group nitrogen, a carboxyl 
group carbon, and a side chain carbon specific for this 
type of amino acid. An exception from this rule is 
proline, where the hydrogen atom is replaced by a bond 
to the side chain. Because the carbon atom is bound to 
four different groups it is chiral, however only one of 
the isomers occur in biological proteins. Glycine 
however, is not chiral since its side chain is a hydrogen 
atom. A simple mnemonic for correct L-form is 
"CORN": when the C atom is viewed with the H in 

a 

front, the residues read "CO-R-N" in a clockwise 
direction. 



R 



C 



a 



,0-H 



\ 



H-N 



H 



C 



O 



An a-amino acid 



' CORN' 




The side chain determines the chemical properties of the 
a-amino acid and may be any one of the 20 different 
side chains: 



The 20 naturally occurring amino acids can be divided 
into several groups based on their chemical properties. 
Important factors are charge, 

hydrophobicity/hydrophilicity, size and functional 
groups. The nature of the interaction of the different side 
chains with the aqueous environment plays a major role 
in molding protein structure. Hydrophobic side chains 
tends to be buried in the middle of the protein, whereas 
hydrophilic side chains are exposed to the solvent. 

Examples of hydrophobic residues are: Leucine, 
isoleucine, phenylalanine, and valine, and to a lesser 
extent tyrosine, alanine and tryptophan. The charge of 
the side chains plays an important role in protein 
structures, since ion bonding can stabilize proteins 
structures, and an unpaired charge in the middle of a 
protein can disrupt structures. Charged residues are strongly hydrophilic, and are usually found on the out side of 
proteins. Positively charged side chains are found in lysine and arginine, and in some cases in histidine. Negative 
charges are found in glutamate and aspartate. The rest of the amino acids have smaller generally hydrophilic side 
chains with various functional groups. Serine and threonine have hydroxyl groups, and aspargine and glutamine have 
amide groups. Some amino acids have special properties such as cysteine, that can form covalent disulfide bonds to 
other cysteines, proline that is cyclical, and glycine that is small, and more flexible than the other amino acids. 



CO-R-N rule 



Protein structure 



163 



The peptide bond (amide bond) 

Two amino acids can be combined in a 
condensation reaction. By repeating this 
reaction, long chains of residues (amino 
acids in a peptide bond) can be generated. 
This reaction is catalysed by the ribosome in 
a process known as translation. The peptide 
bond is in fact planar due to the 
derealization of the electrons from the 
double bond. The rigid peptide dihedral 
angle, to (the bond between C and N) is 
always close to 180 degrees. The dihedral 
angles phi cp (the bond between N and Ca) 
and psi op (the bond between Ca and C ) can 
have a certain range of possible values. 
These angles are the degrees of freedom of a 
protein, they control the protein's three 
dimensional structure. They are restrained 
by geometry to allowed ranges typical for 
particular secondary structure elements, and 
represented in a Ramachandran plot. A few 
important bond lengths are given in the table 
below. 





R 






R' 


H- 


-N ^ 
H 


yO-H 

Two 


imino acids 


N' ^ 

1 O' 
H 



R 

H-N 
H 



H 



O' 



/Ny c; 



r\ 



o 



R' 



Bond angles for i|> and a> 



Peptide bond 


Average length 


Single 
bond 


Average length 


Hydrogen bond 


Average 
(+30) 


Ca-C 


153 pm 


C-C 


154 pm 


OH — O-H 


280 pm 


C-N 


133 pm 


C-N 


148 pm 


N-H — 0=C 


290 pm 


N-Ca 


146 pm 


c-o 


143 pm 


O-H — 0=C 


280 pm 



Side-chain conformation and Rotamers 

The atoms along the side chain are named with Greek letters in Greek alphabetical order: a, |3, y, 6, e, and so on. C 

refers to the carbon atom of the backbone closest to the carbonyl group of that amino acid, C the second closest and 

P 
so on. The C is part of the backbone, while C and atoms further out comprise the side chain. The dihedral angles 

around the bonds between these atoms are named y\, yl, x3, etc. The dihedral angle of the first movable atom of the 

side chain, 7> defined as N-C a-C j3 - X'Y, is named %1. Most side chains can be in different conformations 

called gauche(-), trans, and gauche(+). Side chains generally tend to try to come into a staggered conformation 

around yl, driven by the minimization of the overlap between the electron orbitals of substituent atoms. 

The diversity of side-chain conformations is often expressed in rotamer libraries. A rotamer library is a collection of 

rotamers for each residue type in proteins with side-chain degrees of freedom. Rotamer libraries usually contain 

information about both conformation and frequency of a certain conformation. Often libraries will also contain 



information about the variance about dihedral angle means or modes, which can be used in sampling 



[4] 



Protein structure 164 

Side-chain dihedral angles are not evenly distributed, but for most side chain types, the X angles occur in tight 
clusters around certain values. Rotamer libraries therefore are usually derived from statistical analysis of side-chain 
conformations in known structures of proteins by clustering observed conformations or by dividing dihedral angle 
space into bins, and determining an average conformation in each bin. This division is usually on physical-chemical 
grounds, as in the divisions for rotation about sp3-sp3 bonds into three 120° bins centered on each staggered 
conformation (60°, 180°, -60°). 

Rotamer libraries can be backbone-independent, secondary-structure-dependent, or backbone-dependent. The 
distinctions are made depending on whether the dihedral angles for the rotamers and/or their frequencies depend on 
the local backbone conformation or not. Backbone-independent rotamer libraries make no reference to backbone 
conformation, and are calculated from all available side chains of a certain type. Secondary-structure-dependent 
libraries present different dihedral angles and/or rotamer frequencies for a -helix, (3 -sheet, or coil secondary 
structures. Backbone-dependent rotamer libraries present conformations and/or frequencies dependent on the local 
backbone conformation as defined by the backbone dihedral angles (f) and if} , regardless of secondary structure. 
Finally, a variant on backbone-dependent rotamer libraries exists in the form of position-specific rotamers, those 
defined by a fragment usually of 5 amino acids in length, where the central residue's side chain conformation is 
examined. 

Domains, motifs, and folds in protein structure 

Many proteins are organized into several units. A structural domain is an element of the protein's overall structure 
that is self-stabilizing and often folds independently of the rest of the protein chain. Many domains are not unique to 
the protein products of one gene or one gene family but instead appear in a variety of proteins. Domains often are 
named and singled out because they figure prominently in the biological function of the protein they belong to; for 
example, the "calcium-binding domain of calmodulin". Because they are self-stabilizing, domains can be "swapped" 
by genetic engineering between one protein and another to make chimeras. A motif in this sense refers to a small 
specific combination of secondary structural elements (such as helix-turn-helix). These elements are often called 
supersecondary structures. Fold refers to a global type of arrangement, like helix bundle or beta-barrel. Structure 
motifs usually consist of just a few elements, e.g. the 'helix-turn-helix' has just three. Note that while the spatial 
sequence of elements is the same in all instances of a motif, they may be encoded in any order within the underlying 
gene. Protein structural motifs often include loops of variable length and unspecified structure, which in effect create 
the "slack" necessary to bring together in space two elements that are not encoded by immediately adjacent DNA 
sequences in a gene. Note also that even when two genes encode secondary structural elements of a motif in the 
same order, nevertheless they may specify somewhat different sequences of amino acids. This is true not only 
because of the complicated relationship between tertiary and primary structure, but because the size of the elements 
varies from one protein and the next. Despite the fact that there are about 100,000 different proteins expressed in 
eukaryotic systems, there are much fewer different domains, structural motifs and folds. This is partly a consequence 
of evolution, since genes or parts of genes can be doubled or moved around within the genome. This means that, for 
example, a protein domain might be moved from one protein to another thus giving the protein a new function. 
Because of these mechanisms pathways and mechanisms tends to be reused in several different proteins. 



Protein structure 



165 



Protein folding 

An unfolded polypeptide folds into its characteristic three-dimensional structure from random coil. 

Protein structure determination 

Around 90% of the protein structures available in the Protein Data Bank have been determined by X-ray 
crystallography. This method allows one to measure the 3D density distribution of electrons in the protein (in the 
crystallized state) and thereby infer the 3D coordinates of all the atoms to be determined to a certain resolution. 
Roughly 9% of the known protein structures have been obtained by Nuclear Magnetic Resonance techniques, which 
can also be used to determine secondary structure. Note that aspects of the secondary structure as whole can be 
determined via other biochemical techniques such as circular dichroism or dual polarisation interferometry. 
Secondary structure can also be predicted with a high degree of accuracy (see next section). Cryo-electron 
microscopy has recently become a means of determining protein structures to high resolution (less than 5 angstroms 
or 0.5 nanometer) and is anticipated to increase in power as a tool for high resolution work in the next decade. This 
technique is still a valuable resource for researchers working with very large protein complexes such as virus coat 
proteins and amyloid fibers. 



Resolution 

(A) 



A rough guide to the resolution of protein structures 



Meaning 



>4.0 
3.0-4.0 



Individual coordinates meaningless 

Fold possibly correct, but errors are very likely. Many sidechains placed with wrong rotamer. 



2.5-3.0 



2.0-2.5 



Fold likely correct except that some surface loops might be mismodelled. Several long, thin sidechains (lys, glu, gin, etc) and small 
sidechains (ser, val, thr, etc) likely to have wrong rotamers. 

As 2.5 - 3.0, but number of sidechains in wrong rotamer is considerably less. Many small errors can normally be detected. Fold 
normally correct and number of errors in surface loops is small. Water molecules and small ligands become visible. 



1.5-2.0 



0.5 - 1.5 



Few residues have wrong rotamer. Many small errors can normally be detected. Folds are extremely rarely incorrect, even in surface 
loops. 

In general, structures have almost no errors at this resolution. Rotamer libraries and geometry studies are made from these structures. 



Structure classification 

Protein structures can be classified based on their similarity or a common evolutionary origin. SCOP and CATH 
databases provide two different structural classifications of proteins. 



Computational prediction of protein structure 

The generation of a protein sequence is much simpler than the generation of a protein structure. However, the 
structure of a protein gives much more insight in the function of the protein than its sequence. Therefore, a number 
of methods for the computational prediction of protein structure from its sequence have been proposed. Ab initio 
prediction methods use just the sequence of the protein. Threading uses existing protein structures. Homology 
Modeling to build a reliable 3D model for a protein of unknown structure from one or more related proteins of 
known structure. The recent progress and challenges in protein structure prediction was reviewed by Zhang 



Protein structure 166 

Protein structure related software 

There are software to aid researchers working on, often overlapping, different aspects of protein structure. The most 
basic functionality is providing structure visualization. Analysis of protein structure can be facilitated by software 
that aligns structures. In the absence of existing structures for a given protein sequence, there are methods to predict 
or to model the structure of such sequences based on known protein structures. And given models of known or 
predicted structures, one can use software to verify them for errors, predict protein conformational changes, or 
predict substrate binding sites. 

See also 

• Protein dynamics 

Further reading 

• Chiang YS, Gelfand TI, Kister AE, Gelfand IM (2007). "New classification of supersecondary structures of 
sandwich-like proteins uncovers strict patterns of strand assemblage.". Proteins. 68 (4): 915—921. 
doi:10.1002/prot.21473. PMID 17557333. 

• Habeck M, Nilges M, Rieping W (2005). "Bayesian inference applied to macromolecular structure determination" 

. Physical review. E, Statistical, nonlinear, and soft matter physics 72 (3 Pt 1): 031912. PMID 16241487. 
(Bayesian computational methods for the structure determination from NMR data) 

External links 

• SSS Database — super-secondary structure protein database 

• SPROUTS [10] (Structural Prediction for pRotein folding UTility System) 

• ProSA-web — a web service for the recognition of errors in experimentally or theoretically determined 
protein structures 

ri2i 

• NQ-Flipper — checks for unfavorable rotamers of Asn and Gin residues in protein structures 

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• WHAT IF servers — checks nearly 200 aspects of protein structure, like packing, geometry, unfavourable 

rotamers in general of for Asn, Gin, and His especially, strange water molecules, backbone conformations, atom 
nomenclature, symmetry parameters, etc. 

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• Bioinformatics course — an interactive, fully free, course explaining many of the aspects discussed in this 
wiki entry. 

References 

[1] Brocchieri L, Karlin S (2005-06-10). "Protein length in eukaryotic and prokaryotic proteomes" (http://www.pubmedcentral.nih.gov/ 

articlerender.fcgi?tool=pmcentrez&artid=1150220). Nucleic Acids Research 33 (10): 3390-3400. doi: 10. 1093/nar/gki615. PMID 15951512. 

PMC 1150220. 
[2] Pauling L, Corey RB, Branson HR (1951). "The structure of proteins; two hydrogen-bonded helical configurations of the polypeptide chain" 

(http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1063337). Proc Natl Acad Sci USA 37 (4): 205—211. 

doi:10.1073/pnas.37.4.205. PMID 14816373. PMC 1063337. 
[3] Chiang YS, Gelfand TI, Kister AE, Gelfand IM (2007). "New classification of supersecondary structures of sandwich-like proteins uncovers 

strict patterns of strand assemblage.". Proteins. 68 (4): 915-921. doi:10.1002/prot.21473. PMID 17557333. 
[4] Dunbrack, RL (2002). "Rotamer Libraries in the 21st Century". Curr. Opin. Struct. Biol. 12 (4): 431-440. 

doi:10.1016/S0959-440X(02)00344-5. PMID 12163064. 
[5] Richardson Rotamer Libraries (http://pibs.duke.edu/databases/rotamer.php) 
[6] Dunbrack Rotamer Libraries (http://dunbrack.fccc.edu/bbdep) 
[7] Zhang Y (2008). "Progress and challenges in protein structure prediction" (http://www.pubmedcentral.nih.gov/articlerender. 

fcgi?tool=pmcentrez&artid=2680823). Curr Opin Struct Biol 18 (3): 342-348. doi:10.1016/j.sbi.2008.02.004. Entrez Pubmed 18436442 

(http://www.ncbi. nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=l 8436442). PMID 18436442. 

PMC 2680823. 



Protein structure 



167 



[8] http://www.spineurope.org/publications/Habeck%20et%20al%20031912%202005.pdf 

[9] http://binfs.umdnj .edu/sssdb/ 

[10] http://bioinformatics.eas.asu.edu/springs/Sprouts/projectsSprouts.html 

[11] https://prosa.services.came.sbg.ac.at/prosa.php 

[12] https://flipper.services.came.sbg.ac.at/ 

[13] http://swift.cmbi.ru.nl/ 

[14] http://swift.cmbi.ru.nl/teach/Bl/ 



Protein folding 



Protein folding is the physical process by 
which a polypeptide folds into its 
characteristic and functional 

three-dimensional structure from random 
coil. Each protein exists as an unfolded 
polypeptide or random coil when translated 
from a sequence of mRNA to a linear chain 
of amino acids. This polypeptide lacks any 
developed three-dimensional structure (the 
left hand side of the neighboring figure). 
Amino acids interact with each other to 
produce a well-defined three dimensional structure, the folded protein (the right hand side of the figure), known as 

[2] 

the native state. The resulting three-dimensional structure is determined by the amino acid sequence. 

[3] 

For many proteins the correct three dimensional structure is essential to function. Failure to fold into the intended 
shape usually produces inactive proteins with different properties including toxic prions. Several neurodegenerative 




Protein before and after folding. 



and other diseases are believed to result from the accumulation of misfolded (incorrectly folded) proteins 



[4] 



Protein folding 



168 



Known facts 



Relationship between folding and amino acid sequence 



The amino-acid sequence (or primary 
structure) of a protein defines its native 
conformation. A protein molecule folds 
spontaneously during or after synthesis. 
While these macromolecules may be 
regarded as "folding themselves", the 
process also depends on the solvent (water 
or lipid bilayer), the concentration of salts, 
the temperature, and the presence of 
molecular chaperones. 

Folded proteins usually have a hydrophobic 
core in which side chain packing stabilizes 
the folded state, and charged or polar side 
chains occupy the solvent-exposed surface 
where they interact with surrounding water. 
Minimizing the number of hydrophobic 
side-chains exposed to water is an important 
driving force behind the folding process. 
Formation of intramolecular hydrogen 

bonds provides another important 

[71 
contribution to protein stability. The strength of hydrogen bonds depends on their environment, thus H-bonds 

enveloped in a hydrophobic core contribute more than H-bonds exposed to the aqueous environment to the stability 




Illustration of the main driving force behind protein structure formation. In the 

compact fold (to the right), the hydrophobic amino acids (shown as black spheres) 

are in general shielded from the solvent. 



of the native state 



[81 



In the seminal research work published nearly four decades ago, C.B. Anfinsen hypothesized that "information 

191 
dictating the native fold of protein domains is encoded in their amino acid sequence" . However, with the 

explosive amount of protein sequence, structure, and fold data generated since the time of Anfinsen during the omics 

era, the emerging picture of the protein universe has challenged Anfinsen' s dogma, for it has become evident that 

numerous protein folds have incredible sequence diversity with no consistent "fold code" .In support of this 

observation, recent studies have shown that proteins with as low as 1-2% sequence identity may still adopt the same 

native fold, thus defying any tangible encoding of fold-dictating information into protein sequence . The pursuit 

of the elusive "fold code" has resulted in little more than patterns of amino acid sequence conservations specific to 

certain proteins, but no finding has been compelling enough to generalize universally or to utilize for biological 

applications 

In a recent study, scientists from Harvard-MIT have shown that, despite the enormous diversity within protein folds 
at the level of 1 -dimensional amino acid sequence, nature has encoded fold-conserved information at higher 

dimensions of protein space such as the 2-D (protein contact maps) or 3-D (structure), that are known to be more 

[131 
intricately related to protein folding phenomena . The study published in PLoS ONE illuminated latent 

fold-conserved information from higher dimensional protein space using network theory approaches. By examining 

the entire protein universe on a fold-by-fold basis, the study revealed that atomic interaction networks in the 

solvent-unexposed core of protein domains are fold-conserved and unique to each protein's native fold, thus 

appearing to be the encoded "signature" of protein domains. This study hence uncoverd that the protein fold code is a 

"network phenomena" in addition to a sequence and structural phenomena as commonly presumed. The discovery of 

such a protein folding code also confirms Anfinsens Dogma by proving that a significant portion of the fold-dictating 



Protein folding 169 

information is encoded by the atomic interaction network in the solvent-unexposed core of protein domains. 

The process of folding in vivo often begins co-translationally, so that the N-terminus of the protein begins to fold 
while the C-terminal portion of the protein is still being synthesized by the ribosome. Specialized proteins called 

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chaperones assist in the folding of other proteins. A well studied example is the bacterial GroEL system, which 
assists in the folding of globular proteins. In eukaryotic organisms chaperones are known as heat shock proteins. 
Although most globular proteins are able to assume their native state unassisted, chaperone-assisted folding is often 
necessary in the crowded intracellular environment to prevent aggregation; chaperones are also used to prevent 
misfolding and aggregation which may occur as a consequence of exposure to heat or other changes in the cellular 
environment. 

For the most part, scientists have been able to study many identical molecules folding together en masse. At the 
coarsest level, it appears that in transitioning to the native state, a given amino acid sequence takes on roughly the 
same route and proceeds through roughly the same intermediates and transition states. Often folding involves first 
the establishment of regular secondary and supersecondary structures, particularly alpha helices and beta sheets, and 
afterwards tertiary structure. Formation of quaternary structure usually involves the "assembly" or "coassembly" of 
subunits that have already folded. The regular alpha helix and beta sheet structures fold rapidly because they are 
stabilized by intramolecular hydrogen bonds, as was first characterized by Linus Pauling. Protein folding may 
involve covalent bonding in the form of disulfide bridges formed between two cysteine residues or the formation of 
metal clusters. Shortly before settling into their more energetically favourable native conformation, molecules may 
pass through an intermediate "molten globule" state. 

The essential fact of folding, however, remains that the amino acid sequence of each protein contains the information 
that specifies both the native structure and the pathway to attain that state. This is not to say that nearly identical 
amino acid sequences always fold similarly. Conformations differ based on environmental factors as well; similar 
proteins fold differently based on where they are found. Folding is a spontaneous process independent of energy 
inputs from nucleoside triphosphates. The passage of the folded state is mainly guided by hydrophobic interactions, 
formation of intramolecular hydrogen bonds, and van der Waals forces, and it is opposed by conformational entropy. 

Disruption of the native state 

Under some conditions proteins will not fold into their biochemically functional forms. Temperatures above or 
below the range that cells tend to live in will cause thermally unstable proteins to unfold or "denature" (this is why 
boiling makes an egg white turn opaque). High concentrations of solutes, extremes of pH, mechanical forces, and the 
presence of chemical denaturants can do the same. Protein thermal stability is far from constant, however. For 
example, hyperthermophilic bacteria have been found that grow at temperatures as high as 122°C, which of 
course requires that their full complement of vital proteins and protein assemblies be stable at that temperature or 
above. 

A fully denatured protein lacks both tertiary and secondary structure, and exists as a so-called random coil. Under 

ri7i 
certain conditions some proteins can refold; however, in many cases denaturation is irreversible. Cells sometimes 

protect their proteins against the denaturing influence of heat with enzymes known as chaperones or heat shock 

proteins, which assist other proteins both in folding and in remaining folded. Some proteins never fold in cells at all 

except with the assistance of chaperone molecules, which either isolate individual proteins so that their folding is not 

interrupted by interactions with other proteins or help to unfold misfolded proteins, giving them a second chance to 

refold properly. This function is crucial to prevent the risk of precipitation into insoluble amorphous aggregates. 



Protein folding 170 

Incorrect protein folding and neurodegenerative disease 

Aggregated proteins are associated with prion-related illnesses such as Creutzfeldt-Jakob disease, bovine spongiform 
encephalopathy (mad cow disease), amyloid-related illnesses such as Alzheimer's Disease and familial amyloid 
cardiomyopathy or polyneuropathy, as well as intracytoplasmic aggregation diseases such as Huntington's and 
Parkinson's disease. These age onset degenerative diseases are associated with the multimerization of 

misfolded proteins into insoluble, extracellular aggregates and/or intracellular inclusions including cross-beta sheet 
amyloid fibrils; it is not clear whether the aggregates are the cause or merely a reflection of the loss of protein 
homeostasis, the balance between synthesis, folding, aggregation and protein turnover. Misfolding and excessive 
degradation instead of folding and function leads to a number of proteopathy diseases such as antitrypsin-associated 
Emphysema, cystic fibrosis and the lysosomal storage diseases, where loss of function is the origin of the disorder. 
While protein replacement therapy has historically been used to correct the latter disorders, an emerging approach is 
to use pharmaceutical chaperones to fold mutated proteins to render them functional. 

The Levinthal paradox and Kinetics 

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The Levinthal paradox observes that if a protein were to fold by sequentially sampling all possible conformations, 
it would take an astronomical amount of time to do so, even if the conformations were sampled at a rapid rate (on the 
nanosecond or picosecond scale). Based upon the observation that proteins fold much faster than this, Levinthal then 
proposed that a random conformational search does not occur, and the protein must, therefore, fold through a series 
of meta-stable intermediate states. 

The duration of the folding process varies dramatically depending on the protein of interest. When studied outside 
the cell, the slowest folding proteins require many minutes or hours to fold primarily due to proline isomerization, 
and must pass through a number of intermediate states, like checkpoints, before the process is complete. On the 
other hand, very small single-domain proteins with lengths of up to a hundred amino acids typically fold in a single 
step. Time scales of millisec 
within a few microseconds. 



T211 
step. Time scales of milliseconds are the norm and the very fastest known protein folding reactions are complete 



Energy landscape theory of protein folding 

The protein folding phenomenon was largely an experimental endeavor until the formulation of energy landscape 
theory by Joseph Bryngelson and Peter Wolynes in the late 1980s and early 1990s. This approach introduced the 
principle of minimal frustration, which asserts that evolution has selected the amino acid sequences of natural 
proteins so that interactions between side chains largely favor the molecule's acquisition of the folded state. 
Interactions that do not favor folding are selected against, although some residual frustration is expected to exist. A 
consequence of these evolutionarily selected sequences is that proteins are generally thought to have globally 
"funneled energy landscapes" (coined by Jose Onuchic [reference needed]) that are largely directed towards the 
native state. This "folding funnel" landscape allows the protein to fold to the native state through any of a large 
number of pathways and intermediates, rather than being restricted to a single mechanism. The theory is supported 
by both computational simulations of model proteins and numerous experimental studies, and it has been used to 
improve methods for protein structure prediction and design [reference needed]. The description of protein folding 
by the leveling free-energy landscape is also consistent with the 2 n law of thermodynamics. 



Protein folding 171 

Techniques for studying protein folding 
Circular dichroism 

Circular dichroism is one of the most general and basic tools to study protein folding. Circular dichroism 
spectroscopy measures the absorption of circularly polarized light. In proteins, structures such as alpha helicies and 
beta sheets are chiral, and thus absorb such light. The absorption of this light acts as a marker of the degree of 
foldedness of the protein ensemble. This technique can be used to measure equilibrium unfolding of the protein by 
measuring the change in this absorption as a function of denaturant concentration or temperature. A denaturant melt 
measures the free energy of unfolding as well as the protein's m value, or denaturant dependence. A temperature melt 
measures the melting temperature (T ) of the protein. This type of spectroscopy can also be combined with 
fast-mixing devices, such as stopped flow, to measure protein folding kinetics and to generate chevron plots. 

Vibrational circular dichroism of proteins 

The more recent developments of vibrational circular dichroism (VCD) techniques for proteins, currently involving 
Fourier transform (FFT) instruments, provide powerful means for determining protein conformations in solution 
even for very large protein molecules. Such VCD studies of proteins are often combined with X-ray diffraction of 
protein crystals, FT-IR data for protein solutions in heavy water (DO), or ab initio quantum computations to provide 
unambiguous structural assignments that are unobtainable from CD. 

Modern studies of folding with high time resolution 

The study of protein folding has been greatly advanced in recent years by the development of fast, time-resolved 

techniques. These are experimental methods for rapidly triggering the folding of a sample of unfolded protein, and 

T241 
then observing the resulting dynamics. Fast techniques in widespread use include neutron scattering , ultrafast 

mixing of solutions, photochemical methods, and laser temperature jump spectroscopy. Among the many scientists 

who have contributed to the development of these techniques are Jeremy Cook, Heinrich Roder, Harry Gray, Martin 

Gruebele, Brian Dyer, William Eaton, Sheena Radford, Chris Dobson, Sir Alan R. Fersht and Bengt Nolting. 

Computational prediction of protein tertiary structure 

De novo or ab initio techniques for computational protein structure prediction is related to, but strictly distinct from, 
studies involving protein folding. Molecular Dynamics (MD) is an important tool for studying protein folding and 
dynamics in silico. Because of computational cost, ab initio MD folding simulations with explicit water are limited 
to peptides and very small proteins . MD simulations of larger proteins remain restricted to dynamics of the 

experimental structure or its high-temperature unfolding. In order to simulate long time folding processes (beyond 
about 1 microsecond), like folding of small-size proteins (about 50 residues) or larger, some approximations or 
simplifications in protein models need to be introduced. An approach using reduced protein representation 

(pseudo-atoms representing groups of atoms are defined) and statistical potential is not only useful in protein 

T271 
structure prediction, but is also capable of reproducing the folding pathways. 

There are distributed computing projects which use idle CPU or GPU time of personal computers to solve problems 
such as protein folding or prediction of protein structure. People can run these programs on their computer or 
PlayStation 3 to support them. See links below (for example Folding @ Home) to get information about how to 
participate in these projects. 



Protein folding 172 

Experimental techniques of protein structure determination 

Folded structures of proteins are routinely determined by X-ray crystallography and NMR. 

See also 

Anfinsen's dogma 

1281 

Harvard-MIT Scientists Discover the Protein Folding Code and demonstrate this is a Network phenomenon 

Chevron plot 

Denaturation (biochemistry) 

Denaturation midpoint 

Downhill folding 

Folding (chemistry) 

Folding© Home 

Foldit computer game 

Levinthal paradox 

Protein design 

Protein dynamics 

Protein Misfolding Cyclic Amplification 

Protein structure prediction 

Protein structure prediction software 

Rosetta@home 

Software for molecular mechanics modeling 

External links 

[291 

• Foldit - Folding Protein Game 

• Folding® Home 

• Rosetta@Home [31] 

References 

[1] Alberts, Bruce; Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and Peter Walters (2002). "The Shape and Structure of 

Proteins" (http://www.ncbi.nlm.nih. gov/ entrez/query.fcgi?cmd=Search&db=books&doptcmdl=GenBookHL&term=mboc4[book]+ 

AND+372270[uid]&rid=mboc4. section. 388). Molecular Biology of the Cell; Fourth Edition. New York and London: Garland Science. 

ISBN 0-8153-3218-1.. 
[2] Anfinsen, C. (1972). "The formation and stabilization of protein structure" (http://www.pubmedcentral.nih.gov/articlerender. 

fcgi?tool=pmcentrez&artid=l 173893). Biochem. J. 128 (4): 737^9. PMID 4565 129. PMC 1173893. 
[3] Jeremy M. Berg, John L. Tymoczko, Lubert Stryer; Web content by Neil D. Clarke (2002). "3. Protein Structure and Function" (http://www. 

ncbi. nlm.nih.gov/entrez/ query. fcgi?cmd=Search&db=books&doptcmdl=GenBookHL&term=stryer[book]+AND+215168[uid]& 

rid=stryer.chapter.280). Biochemistry. San Francisco: W. H. Freeman. ISBN 0-7167-4684-0. . 
[4] Dennis J. Selkoe (2003). "Folding proteins in fatal ways" (http://www.nature.com/nature/journal/v426/n6968/full/nature02264.html). 

Nature 426: pp. 900-904. doi:10.1038/nature02264. PMID 14685251. . 
[5] van den Berg, B., Wain, R., Dobson, C. M., Ellis R. J. (August 2000). "Macromolecular crowding perturbs protein refolding kinetics: 

implications for folding inside the cell" (http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=306593). EMBO J. 

19 (15): 3870-5. doi: 10. 1093/emboj/19. 15.3870. PMID 10921869. PMC 306593. 
[6] Pace, C, Shirley, B., McNutt, M., Gajiwala, K. (1 January 1996). "Forces contributing to the conformational stability of proteins" (http:// 

www.fasebj.org/cgi/reprint/10/1/75). FASEB J. 10 (1): 75-83. PMID 8566551. . 
[7] Rose, G., Fleming, P., Banavar, J., Maritan, A. (2006). "A backbone-based theory of protein folding" (http://www.pubmedcentral.nih.gov/ 

articlerender.fcgi?tool=pmcentrez&artid=1636505). Proc. Natl. Acad. Sci. U.S.A. 103 (45): 16623-33. doi:10.1073/pnas.0606843103. 

PMID 17075053. PMC 1636505. 
[8] Deechongkit, S., Nguyen, H., Dawson, P. E., Gruebele, M., Kelly, J. W. (2004). "Context Dependent Contributions of Backbone H-Bonding 

to [5-Sheet Folding Energetics" (http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1636505). Nature 403 (45): 

101-5. doi:10.1073/pnas.0606843103. PMID 17075053. PMC 1636505. 



Protein folding 173 

[9] Anfinsen CB. (20 July 1973). "Principles that Govern the Folding of Protein Chains" (http://www.sciencemag.org/cgi/pdf_extract/181/ 

4096/223). Science. 181 (96): 223-230. doi:10.1126/science.l81.4096.223. PMID4124164. . 
[10] Govindarajan S, Recabarren R, Goldstein RA. (17 Sep 1999). "Estimating the total number of protein folds." (http://www3.interscience. 

wiley.com/journal/65000323/abstract). Proteins. 35 (4): 408-414. 

doi:10.1002/(SICI)1097-0134(19990601)35:4<408::AID-PROT4>3.0.CO;2-A. PMID 10382668. . 
[11] Mirny, L. A., Abkevich, V. I. & Shakhnovich, E. I. (28 Apr 1998). "How evolution makes proteins fold quickly." (http://www.pnas.org/ 

content/95/9/4976. abstract). Proc Natl Acad Sci U S A. 95 (9): 4976^981. doi:10.1073/pnas.95.9.4976. PMID 9560213. PMC 20198. . 
[12] S Rackovsky. (15 Jan 1993). "On the nature of the protein folding code." (http://www.pnas.Org/content/90/2/644.abstract). Proc Natl 

AcadSciUSA. 90 (2): 644-648. doi:10.1073/pnas.90.2.644. PMID 8421700. PMC 45720. . 
[13] Venkataramanan Soundararajan, Rahul Raman, S. Raguram, V. Sasisekharan, Ram Sasisekharan (2010). "Atomic Interaction Networks in 

the Core of Protein Domains and Their Native Folds" (http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez& 

artid=2826414). PLoS ONE 5 (2): e9391. doi:10.1371/journal.pone.0009391. PMID 20186337. PMC 2826414. 
[14] Lee, S., Tsai, F. (2005). "Molecular chaperones in protein quality control" (http://www.jbmb. or.kr/fulltext/jbmb/view.php?vol=38& 

page=259). J. Biochem. Mol. Biol. 38 (3): 259-65. PMID 15943899. . 
[15] Alexander, P. A., He Y., Chen, Y., Orban, J., Bryan, P. N. (2007). "The design and characterization of two proteins with 88% sequence 

identity but different structure and function" (http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1906725). 

Proc Natl Acad Sci USA. 104 (29): 11963-8. doi:10.1073/pnas.0700922104. PMID 17609385. PMC 1906725. 
[16] Takai, K., Nakamura, K., Toki, T., Tsunogai, U., Miyazaki, M., Miyazaki, J., Hirayama, H., Nakagawa, S., Nunoura, T., Horikoshi, K. 

(2008). "Cell proliferation at 122°C and isotopically heavy CH4 production by a hyperthermophilic methanogen under high-pressure 

cultivation" (http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2490668). Proc Natl Acad Sci USA 105 (31): 

10949-54. doi:10.1073/pnas.0712334105. PMID 18664583. PMC 2490668. 
[17] Shortle, D. (1 January 1996). "The denatured state (the other half of the folding equation) and its role in protein stability" (http://www. 

fasebj.org/cgi/reprint/10/1/27). FASEB J. 10 (1): 27-34. PMID 8566543. . 
[18] Chiti, F.; Dobson, C. (2006). "Protein misfolding, functional amyloid, and human disease.". Annual review of biochemistry 75: 333—366. 

doi:10.1146/annurev.biochem.75.101304.123901. PMID 16756495. 
[19] C. Levinthal (1968). "Are there pathways for protein folding?" (http://www.biochem.wisc.edu/courses/biochem704/Reading/ 

Levinthall968.pdf). J. Chim. Phys. 65: 44-5. . 
[20] Kim, P. S., Baldwin, R. L. (1990). "Intermediates in the folding reactions of small proteins". Annu. Rev. Biochem. 59: 631—60. 

doi:10.1146/annurev.bi.59.070190.003215. PMID 2197986. 
[21] Jackson S. E. (August 1998). "How do small single-domain proteins fold?" (http://biomednet.com/elecref/13590278003R0081). Fold Des 

3 (4): R81-91. doi:10.1016/S1359-0278(98)00033-9. PMID 9710577. . 
[22] Kubelka, J., Hofrichter, J., Eaton, W. A. (February 2004). "The protein folding 'speed limit'". Curr. Opin. Struct. Biol. 14 (1): 76—88. 

doi:10.1016/j.sbi.2004.01.013. PMID 15102453. 
[23] Sharma, V., Kaila, V. R. I., and Annila, A. (2009). "Protein folding as an evolutionary process". Physica A 388 (6): 851—862. 

doi:10.1016/j.physa.2008.12.004. 
[24] Bu, Z; Cook, J; Callaway, D. J. E. (2001). "Dynamic regimes and correlated structural dynamics in native and denatured 

alpha-lactalbuminC". JMolBioliU (4): 865-873. doi:10.1006/jmbi.2001.5006. PMID 11575938. 
[25] "Fragment-based Protein Folding Simulations" (http://www.cs.ucl.ac.Uk/staff/d.jones/t42morph.html). . 
[26] "Protein folding" (http://www.biomolecular-modeling.com/Abalone/Protein-folding.html) (by Molecular Dynamics). . 
[27] Kmiecik, S., and Kolinski, A. (2007). "Characterization of protein-folding pathways by reduced-space modeling" (http://www. 

pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1941469). Proc. Natl. Acad. Sci. U.S.A. 104 (30): 12330—5. 

doi:10.1073/pnas.0702265104. PMID 17636132. PMC 1941469. 
[28] http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0009391 
[29] http://fold.it/portal/info/science 

[30] http://www.stanford.edu/group/pandegroup/folding/about.html 
[31] http://boinc.bakerlab.org/rosetta 



Protein dynamics 



174 



Protein dynamics 



A protein domain is a part of protein sequence and 
structure that can evolve, function, and exist 
independently of the rest of the protein chain. Each 
domain forms a compact three-dimensional structure 
and often can be independently stable and folded. 
Many proteins consist of several structural domains. 
One domain may appear in a variety of evolutionarily 
related proteins. Domains vary in length from between 
about 25 amino acids up to 500 amino acids in length. 
The shortest domains such as zinc fingers are stabilized 
by metal ions or disulfide bridges. Domains often form 
functional units, such as the calcium-binding EF hand 
domain of calmodulin. Because they are self-stable, 
domains can be "swapped" by genetic engineering 
between one protein and another to make chimeric 
proteins. 

Background 

The concept of the domain was first proposed in 1973 
by Wetlaufer after X-ray crystallographic studies of hen 
lysozyme and papain and by limited proteolysis 

[4] [5] 




Pyruvate kinase, a protein from three domains (PDB lpkn ) 



studies of immunoglobulins . Wetlaufer defined 

domains as stable units of protein structure that could fold autonomously. In the past domains have been described as 

units of: 



compact structure 
function and evolution 1 

[8] 



[7] 



• folding 

Each definition is valid and will often overlap, i.e. a compact structural domain that is found amongst diverse 
proteins is likely to fold independently within its structural environment. Nature often brings several domains 
together to form multidomain and multifunctional proteins with a vast number of possibilities . In a multidomain 
protein, each domain may fulfil its own function independently, or in a concerted manner with its neighbours. 
Domains can either serve as modules for building up large assemblies such as virus particles or muscle fibres, or can 
provide specific catalytic or binding sites as found in enzymes or regulatory proteins. 

An appropriate example is pyruvate kinase, a glycolytic enzyme that plays an important role in regulating the flux 
from fructose- 1,6-biphosphate to pyruvate. It contains an all-|3 regulatory domain, an a/p-substrate binding domain 
and an a/p-nucleotide binding domain, connected by several polypeptide linkers (see figure, right). Each domain 
in this protein occurs in diverse sets of protein families. 

The central a/p-barrel substrate binding domain is one of the most common enzyme folds. It is seen in many 
different enzyme families catalysing completely unrelated reactions . The a/p-barrel is commonly called the TIM 
barrel named after triose phosphate isomerase, which was the first such structure to be solved . It is currently 
classified into 26 homologous families in the CATH domain database . The TIM barrel is formed from a 

sequence of p-a-p motifs closed by the first and last strand hydrogen bonding together, forming an eight stranded 



Protein dynamics 175 

barrel. There is debate about the evolutionary origin of this domain. One study has suggested that a single ancestral 

ri4i 
enzyme could have diverged into several families , while another suggests that a stable TIM-barrel structure has 

evolved through convergent evolution 

The TIM-barrel in pyruvate kinase is 'discontinuous', meaning that more than one segment of the polypeptide is 
required to form the domain. This is likely to be the result of the insertion of one domain into another during the 
protein's evolution. It has been shown from known structures that about a quarter of structural domains are 
discontinuous. The inserted p-barrel regulatory domain is 'continuous', made up of a single stretch of 

polypeptide. 

Covalent association of two domains represents a functional and structural advantage since there is an increase in 

no] 

stability when compared with the same structures non-covalently associated . Other, advantages are the 

protection of intermediates within inter-domain enzymatic clefts that may otherwise be unstable in aqueous 

environments, and a fixed stoichiometric ratio of the enzymatic activity necessary for a sequential set of reactions 

[19] 

Domains are units of protein structure 
Primary structure 

The primary structure (string of amino acids) of a protein encodes its uniquely folded 3D conformation. The most 
important factor governing the folding of a protein into 3D structure is the distribution of polar and non-polar side 
chains. Folding is driven by the burial of hydrophobic side chains into the interior of the molecule so to avoid 
contact with the aqueous environment. 

Sequence alignment is an important tool for determining domains. 

Secondary structure 

Generally proteins have a core of hydrophobic residues surrounded by a shell of hydrophilic residues. Since the 
peptide bonds themselves are polar they are neutralised by hydrogen bonding with each other when in the 
hydrophobic environment. This gives rise to regions of the polypeptide that form regular 3D structural patterns 
called 'secondary structure'. There are two main types of secondary structure: 

• a-helices 

• p-sheet 

Secondary structure motifs 

Some simple combinations of secondary structure elements have been found to frequently occur in protein structure 
and are referred to as 'super-secondary structure' or motifs. For example, the p-hairpin motif consists of two adjacent 
antiparallel p-strands joined by a small loop. It is present in most antiparallel p structures both as an isolated ribbon 
and as part of more complex p-sheets. Another common super-secondary structure is the P-a-P motif, which is 
frequently used to connect two parallel p-strands. The central a-helix connects the C-termini of the first strand to the 
N-termini of the second strand, packing its side chains against the p-sheet and therefore shielding the hydrophobic 
residues of the p-strands from the surface. 



Protein dynamics 176 

Tertiary structure 

Several motifs pack together to form compact, local, semi-independent units called domains. The overall 3D 
structure of the polypeptide chain is referred to as the protein's 'tertiary structure'. Domains are the fundamental units 
of tertiary structure, each domain containing an individual hydrophobic core built from secondary structural units 
connected by loop regions. The packing of the polypeptide is usually much tighter in the interior than the exterior of 

T221 

the domain producing a solid-like core and a fluid-like surface. In fact, core residues are often conserved in a 
protein family, whereas the residues in loops are less conserved, unless they are involved in the protein's function. 
Protein tertiary structure can be divided into four main classes based on the secondary structural content of the 
domain. 

• All-a domains have a domain core built exclusively from cc-helices. This class is dominated by small folds, many 
of which form a simple bundle with helices running up and down. 

• All-p domains have a core comprising of antiparallel p-sheets, usually two sheets packed against each other. 

Various patterns can be identified in the arrangement of the strands, often giving rise to the identification of 

T241 
recurring motifs, for example the Greek key motif. 

• a+p domains are a mixture of all-a and all-p motifs. Classification of proteins into this class is difficult because 

ri3i 

of overlaps to the other three classes and therefore is not used in the CATH domain database. 

• a/p domains are made from a combination of p-a-p motifs that predominantly form a parallel p-sheet surrounded 
by amphipathic a-helices. The secondary structures are arranged in layers or barrels. 

Structural alignment is an important tool for determining domains. 

Domains have limits on size 

T251 
Domains have limits on size. The size of individual structural domains varies from 36 residues in E-selectin to 

692 residues in lipoxygenase- 1, but the majority, 90%, have less than 200 residues with an average of 

approximately 100 residues. Very short domains, less than 40 residues, are often stabilised by metal ions or 

rofil 

disulfide bonds. Larger domains, greater than 300 residues, are likely to consist of multiple hydrophobic cores. 

Relationship between primary and tertiary structure 
Modules 

[291 
Nature is a tinkerer and not an inventor, new sequences are adapted from pre-existing sequences rather than 

invented. Domains are the common material used by nature to generate new sequences, they can be thought of as 

genetically mobile units, referred to as 'modules'. Often, the C and N termini of domains are close together in space, 

allowing them to easily be "slotted into" parent structures during the process of evolution. Many domain families are 

found in all three forms of life, Archaea, Bacteria and Eukarya. Domains that are repeatedly found in diverse 

proteins are often referred to as modules, examples can be found among extracellular proteins associated with 

clotting, fibrinolysis, complement, the extracellular matrix, cell surface adhesion molecules and cytokine 

[30] 

receptors. 

Protein families 

Molecular evolution gives rise to families of related proteins with similar sequence and structure. However, sequence 
similarities can be extremely low between proteins that share the same structure. Protein structures may be similar 
because proteins have diverged from a common ancestor. Alternatively, some folds may be more favored than others 
as they represent stable arrangements of secondary structures and some proteins may converge towards these folds 
over the course of evolution . There are currently about 45,000 experimentally determined protein 3D structures 
deposited within the Protein Data Bank (PDB). However this set contains a lot of identical or very similar 
structures. All proteins should be classified to structural families to understand their evolutionary relationships. 



Protein dynamics 177 

Structural comparisons are best achieved at the domain level. For this reason many algorithms have been developed 
to automatically assign domains in proteins with known 3D structure, see 'Domain definition from structural 
co-ordinates'. 

Super-folds 

The CATH domain database classifies domains into approximately 800 fold families, ten of these folds are highly 

populated and are referred to as 'super-folds'. Super-folds are defined as folds for which there are at least three 

T321 
structures without significant sequence similarity. The most populated is the a/p-barrel super-fold as described 

previously. 

Multidomain proteins 

The majority of genomic proteins, two-thirds in unicellular organisms and more than 80% in metazoa, are 

[33] 
multidomain proteins created as a result of gene duplication events. Many domains in multidomain structures 

could have once existed as independent proteins. More and more domains in eukaryotic multidomain proteins can be 

found as independent proteins in prokaryotes. For example, vertebrates have a multi-enzyme polypeptide 

containing the GAR synthetase, AIR synthetase and GAR transformylase modules (GARs-AIRs-GARt; GAR: 

glycinamide ribonucleotide synthetase/transferase; AIR: aminoimidazole ribonucleotide synthetase). In insects, the 

polypeptide appears as GARs-(AIRs)2-GARt, in yeast GARs-AIRs is encoded separately from GARt, and in 

T351 
bacteria each domain is encoded separately. 

Origin 

Multidomain proteins are likely to have emerged from a selective pressure during evolution to create new functions. 
Various proteins have diverged from common ancestors by different combinations and associations of domains. 
Modular units frequently move about, within and between biological systems through mechanisms of genetic 
shuffling: 

• transposition of mobile elements including horizontal transfers (between species); 

• gross rearrangements such as inversions, translocations, deletions and duplications; 

• homologous recombination; 

• slippage of DNA polymerase during replication. 

Difference in proliferation 

It is likely that all these and organisms. For example, the ABC transporter domain constitutes one of the largest 

[35] 
domain families that appear in all organisms. Many other families that appear in all organisms show much less 

proliferation. These include metabolic enzymes and components of translational apparatus. 

Types of organisation 

T371 
The simplest multidomain organisation seen in proteins is that of a single domain repeated in tandem. The 

domains may interact with each other or remain isolated, like beads on string. The giant 30,000 residue muscle 

T3R1 

protein titin comprises about 120 fibronectin-III-type and Ig-type domains. In the serine proteases, a gene 

[39] 
duplication event has led to the formation of a two p-barrel domain enzyme. The repeats have diverged so widely 

that there is no obvious sequence similarity between them. The active site is located at a cleft between the two 

p-barrel domains, in which functionally important residues are contributed from each domain. Genetically 

engineered mutants of the chymotrypsin serine protease were shown to have some proteinase activity even though 

their active site residues were abolished and it has therefore been postulated that the duplication event enhanced the 

<•■ •<• [39] 
enzyme s activity. 



Protein dynamics 178 

Connectivity 

Modules frequently display different connectivity relationships, as illustrated by the kinesins and ABC transporters. 
The kinesin motor domain can be at either end of a polypeptide chain that includes a coiled-coil region and a cargo 
domain. ABC transporters are built with up to four domains consisting of two unrelated modules, ATP-binding 
cassette and an integral membrane module, arranged in various combinations. 

Domain insertion 

Not only do domains recombine, but there are many examples of a domain having been inserted into another. 
Sequence or structural similarities to other domains demonstrate that homologues of inserted and parent domains can 
exist independently. An example is that of the 'fingers' inserted into the 'palm' domain within the polymerases of the 
Pol I family. [41] 

Difference between structural and evolutionary domain 

Since a domain can be inserted into another, there should always be at least one continuous domain in a multidomain 
protein. This is the main difference between definitions of structural domains and evolutionary/functional domains. 
An evolutionary domain will be limited to one or two connections between domains, whereas structural domains can 
have unlimited connections, within a given criterion of the existence of a common core. Several structural domains 
could be assigned to an evolutionary domain. 

Domains are autonomous folding units 
Folding 

History 

Protein folding - the unsolved problem 

Since the seminal work of Anfinsen over forty years ago, the goal to completely understand the mechanism 
by which a polypeptide rapidly folds into its stable native conformation remains elusive. Many experimental 
folding studies have contributed much to our understanding, but the principles that govern protein folding are 
still based on those discovered in the very first studies of folding. Anfinsen showed that the native state of a 
protein is thermodynamically stable, the conformation being at a global minimum of its free energy. 

Folding pathway 

Folding is a directed search of conformational space allowing the protein to fold on a biologically feasible time scale. 

The Levinthal paradox states that if an averaged sized protein would sample all possible conformations before 

T421 
finding the one with the lowest energy, the whole process would take billions of years. Proteins typically fold 

within 0.1 and 1000 seconds, therefore the protein folding process must be directed some way through a specific 

folding pathway. The forces that direct this search are likely to be a combination of local and global influences 

whose effects are felt at various stages of the reaction. 

Advances in experimental and theoretical studies have shown that folding can be viewed in terms of energy 

[44] [451 

landscapes, where folding kinetics is considered as a progressive organisation of an ensemble of partially 

folded structures through which a protein passes on its way to the folded structure. This has been described in terms 
of a folding funnel, in which an unfolded protein has a large number of conformational states available and there are 
fewer states available to the folded protein. A funnel implies that for protein folding there is a decrease in energy and 
loss of entropy with increasing tertiary structure formation. The local roughness of the funnel reflects kinetic traps, 
corresponding to the accumulation of misfolded intermediates. A folding chain progresses toward lower intra-chain 
free-energies by increasing its compactness. The chains conformational options become increasingly narrowed 



Protein dynamics 179 

ultimately toward one native structure. 

Advantage of domains in protein folding 

The organisation of large proteins by structural domains represents an advantage for protein folding, with each 
domain being able to individually fold, accelerating the folding process and reducing a potentially large combination 
of residue interactions. Furthermore, given the observed random distribution of hydrophobic residues in proteins, 
domain formation appears to be the optimal solution for a large protein to bury its hydrophobic residues while 
keeping the hydrophilic residues at the surface. 

However, the role of inter-domain interactions in protein folding and in energetics of stabilisation of the native 

structure, probably differs for each protein. In T4 lysozyme, the influence of one domain on the other is so strong 

that the entire molecule is resistant to proteolytic cleavage. In this case, folding is a sequential process where the 

C-terminal domain is required to fold independently in an early step, and the other domain requires the presence of 

[49] 
the folded C-terminal domain for folding and stabilisation. 

It has been found that the folding of an isolated domain can take place at the same rate or sometimes faster than that 
of the integrated domain. Suggesting that unfavourable interactions with the rest of the protein can occur during 
folding. Several arguments suggest that the slowest step in the folding of large proteins is the pairing of the folded 

no] 

domains. This is either because the domains are not folded entirely correctly or because the small adjustments 
required for their interaction are energetically unfavourable, such as the removal of water from the domain 
interface. 

Domains and quaternary structure 
About quaternary structures 

Many proteins have a quaternary structure, which consists of several polypeptide chains that associate into an 
oligomeric molecule. Each polypeptide chain in such a protein is called a subunit. Hemoglobin, for example, consists 
of two a and two p subunits. Each of the four chains has an all-a globin fold with a heme pocket. 

Domain swapping 

T521 

Domain swapping is a mechanism for forming oligomeric assemblies. . In domain swapping, a secondary or 
tertiary element of a monomeric protein is replaced by the same element of another protein. Domain swapping can 

range from secondary structure elements to whole structural domains. It also represents a model of evolution for 

T531 
functional adaptation by oligomerisation, e.g. oligomeric enzymes that have their active site at subunit interfaces. 

Domains and protein flexibility 

The presence of multiple domains in proteins gives rise to a great deal of flexibility and mobility, leading to protein 
domain dynamics. Domain motions can be inferred by comparing structures of a protein in different environments, 

[541 

or directly observed using spectra measured by neutron spin echo spectroscopy. One of the largest observed 
domain motions is the "swivelling' mechanism in pyruvate phosphate dikinase. The phosphoinositide domain swivels 
between two states in order to bring a phosphate group from the active site of the nucleotide binding domain to that 
of the phosphoenolpyruvate/pyruvate domain. The phosphate group is moved over a distance of 45 A involving a 
domain motion of about 100 degrees around a single residue. Domain motions are important for: 

• catalysis; 

• regulatory activity; 

• transport of metabolites; 

• formation of protein assemblies; and 



Protein dynamics 180 

• cellular locomotion. 

In enzymes, the closure of one domain onto another captures a substrate by an induced fit, allowing the reaction to 
take place in a controlled way. A detailed analysis by Gerstein led to the classification of two basic types of domain 
motion; hinge and shear. Only a relatively small portion of the chain, namely the inter-domain linker and side 
chains undergo significant conformational changes upon domain rearrangement. 

Hinges by secondary structures 

rcon 

A study by Hayward found that the termini of a-helices and p-sheets form hinges in a large number of cases. 
Many hinges were found to involve two secondary structure elements acting like hinges of a door, allowing an 
opening and closing motion to occur. This can arise when two neighbouring strands within a p-sheet situated in one 
domain, diverge apart as they join the other domain. The two resulting termini then form the bending regions 
between the two domains, a-helices that preserve their hydrogen bonding network when bent are found to behave as 

rco] 

mechanical hinges, storing "elastic energy' that drives the closure of domains for rapid capture of a substrate. 

Helical to extended conformation 

The interconversion of helical and extended conformations at the site of a domain boundary is not uncommon. In 
calmodulin, torsion angles change for five residues in the middle of a domain linking a-helix. The helix is split into 
two, almost perpendicular, smaller helices separated by four residues of an extended strand. 

Shear motions 

Shear motions involve a small sliding movement of domain interfaces, controlled by the amino acid side chains 
within the interface. Proteins displaying shear motions often have a layered architecture: stacking of secondary 
structures. The interdomain linker has merely the role of keeping the domains in close proximity. 

Domain definition from structural co-ordinates 

The importance of domains as structural building blocks and elements of evolution has brought about many 
automated methods for their identification and classification in proteins of known structure. Automatic procedures 
for reliable domain assignment is essential for the generation of the domain databases, especially as the number of 
protein structures is increasing. Although the boundaries of a domain can be determined by visual inspection, 
construction of an automated method is not straightforward. Problems occur when faced with domains that are 
discontinuous or highly associated. The fact that there is no standard definition of what a domain really is has 
meant that domain assignments have varied enormously, with each researcher using a unique set of criteria. 

A structural domain is a compact, globular sub-structure with more interactions within it than with the rest of the 
protein. Therefore, a structural domain can be determined by two visual characteristics; its compactness and its 
extent of isolation. Measures of local compactness in proteins have been used in many of the early methods of 

a ■ ■ J64] [65] [66] [67] . . , ,., ., , [26] [68] [69] [70] [71] 

domain assignment and in several of the more recent methods. 

Considering proteins as small segments 

One of the first algorithms used a Ca-Ca distance map together with a hierarchical clustering routine that 
considered proteins as several small segments, 10 residues in length. The initial segments were clustered one after 
another based on inter-segment distances; segments with the shortest distances were clustered and considered as 
single segments thereafter. The stepwise clustering finally included the full protein. Go also exploited the fact that 
inter-domain distances are normally larger than intra-domain distances; all possible Ca-Ca distances were 
represented as diagonal plots in which there were distinct patterns for helices, extended strands and combinations of 
secondary structures. 



Protein dynamics 181 

Sowdhamini and Blundell's method 

The method by Sowdhamini and Blundell clusters secondary structures in a protein based on their Ca-Ca distances 
and identifies domains from the pattern in their dendrograms. As the procedure does not consider the protein as a 
continuous chain of amino acids there are no problems in treating discontinuous domains. Specific nodes in these 
dendrograms are identified as tertiary structural clusters of the protein, these include both super-secondary structures 
and domains. The DOMAK algorithm is used to create the 3Dee domain database. It calculates a 'split value' from 
the number of each type of contact when the protein is divided arbitrarily into two parts. This split value is large 
when the two parts of the structure are distinct. 

Method of Wodak and Janin 

T721 
The method of Wodak and Janin was based on the calculated interface areas between two chain segments 

repeatedly cleaved at various residue positions. Interface areas were calculated by comparing surface areas of the 

cleaved segments with that of the native structure. Potential domain boundaries can be identified at a site where the 

interface area was at a minimum. 

Other methods have used measures of solvent accessibility to calculate compactness. 

PUU algorithm 

ri7i 

The PUU algorithm incorporates a harmonic model used to approximate inter-domain dynamics. The underlying 
physical concept is that many rigid interactions will occur within each domain and loose interactions will occur 
between domains. This algorithm is used to define domains in the FSSP domain database. 

DETECTIVE 

Swindells (1995) developed a method, DETECTIVE, for identification of domains in protein structures based on the 
idea that domains have a hydrophobic interior. Deficiencies were found to occur when hydrophobic cores from 
different domains continue through the interface region. 

RigidFinder 

T751 
RigidFinder is a novel method for identification of protein rigid blocks (domains and loops) from two different 

conformations. Rigid blocks are defined as blocks where all inter residue distances are conserved across 

conformations. 

PiSQRD 

The PiSQRD web-server allows users to optimally subdivide single-chain or multimeric proteins into domains 

T771 T7S1 - 

that behave approximately as rigid units in the course of protein structural fluctuations . The best rigid-body 

decomposition is found using the lowest-energy collective modes of the system. By default the latter are calculated 
through an elastic network model, or can be uploaded by the user. 



Protein dynamics 182 

Example domains 

Armadillo repeats 

named after the p-catenin-like Armadillo protein of the fruit fly Drosophila. 

Basic Leucine zipper domain (bZIP domain) 

is found in many DNA-binding eukaryotic proteins. One part of the domain contains a region that mediates 
sequence-specific DNA-binding properties and the Leucine zipper that is required for the dimerization of two 
DNA-binding regions. The DNA-binding region comprises a number of basic aminoacids such as arginine and 
lysine 

Cadherin repeats 

Cadherins function as Ca -dependent cell-cell adhesion proteins. Cadherin domains are extracellular regions 
which mediate cell-to-cell homophilic binding between cadherins on the surface of adjacent cells. 

Death effector domain (DED) 

allows protein-protein binding by homotypic interactions (DED-DED). Caspase proteases trigger apoptosis via 
proteolytic cascades. Pro-Caspase-8 and pro-caspase-9 bind to specific adaptor molecules via DED domains 
and this leads to autoactivation of caspases. 

EF hand 

a helix-turn-helix structural motif found in each structural domain of the signaling protein calmodulin and in 
the muscle protein troponin-C. 

Immunoglobulin-like domains 

[79] 
are found in proteins of the immunoglobulin superfamily (IgSF). They contain about 70-110 amino acids 

and are classified into different categories (IgV, IgCl, IgC2 and Igl) according to their size and function. They 

possess a characteristic fold in which two beta sheets form a "sandwich" that is stabilized by interactions 

between conserved cysteines and other charged amino acids. They are important for protein-to-protein 

interactions in processes of cell adhesion, cell activation, and molecular recognition. These domains are 

commonly found in molecules with roles in the immune system. 

Phosphotyrosine-binding domain (PTB) 

PTB domains usually bind to phosphorylated tyrosine residues. They are often found in signal transduction 
proteins. PTB-domain binding specificity is determined by residues to the amino-terminal side of the 
phosphotyrosine. Examples: the PTB domains of both SHC and IRS-1 bind to a NPXpY sequence. 
PTB -containing proteins such as SHC and IRS-1 are important for insulin responses of human cells. 

Pleckstrin homology domain (PH) 

PH domains bind phosphoinositides with high affinity. Specificity for PtdIns(3)P, PtdIns(4)P, PtdIns(3,4)P2, 
PtdIns(4,5)P2, and PtdIns(3,4,5)P3 have all been observed. Given the fact that phosphoinositides are 
sequestered to various cell membranes (due to their long lipophilic tail) the PH domains usually causes 
recruitment of the protein in question to a membrane where the protein can exert a certain function in cell 
signalling, cytoskeletal reorganization or membrane trafficking. 

Src homology 2 domain (SH2) 

SH2 domains are often found in signal transduction proteins. SH2 domains confer binding to phosphorylated 
tyrosine (pTyr). Named after the phosphotyrosine binding domain of the src viral oncogene, which is itself a 
tyrosine kinase. See also: SH3 domain. 

Zinc finger DNA binding domain (ZnF_GATA) 

ZnF_GATA domain-containing proteins are typically transcription factors that usually bind to the DNA 
sequence [AT] GAT A [AG] of promoters. 



Protein dynamics 183 

The preceding text and figures originate from "Predicting Structural Domains in Proteins" George RA, 2002. 

See also 

Amino acid 

Binding domain 

CATH 

Conserved domains 

Motif domain 

Eukaryotic Linear Motif 

Protein 

Protein structure 

Protein structure prediction 

Protein structure prediction software 

Protein family 

Structural biology 

Structural Classification of Proteins (SCOP) 

Structural domain databases 

3Dee [80] 

CATH [81] 

DALI [82] 

SCOP [83] 

Pawson Lab - Protein interaction domains 

roc] 

Nash Lab - Protein interaction domains in Signal Transduction 
Definition and assignment of structural domains in proteins 



Sequence domain databases 

'ro [f 

[88] 



InterPro 



Pfam 

[90] 



PROSITE [89] 



ProDom 

[91] 

[92] 



SMART [91] 



NCBI Conserved Domain Database 

[93] 
SUPERFAMILY Library of HMMs representing superfamilies and database of (superfamily and family) 

annotations for all completely sequenced organisms 



Protein dynamics 184 

External links 

[941 
• The Protein Families (Pfam) database clan browser provides easy access to information about protein 

structural domains. A clan contains two or more Pfam families that have arisen from a single evolutionary origin. 

Key papers 

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[971 
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Protein dynamics 185 

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doi:10.1002/pro.5560060609. PMID 9194181. PMC 2143719. 
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[72] Wodak, S. J. and Janin, J (1981). ""Location of structural domains in protein"". Biochemistry 20 (23): 6544—6552. 

doi:10.1021/bi00526a005. PMID 7306523. 
[73] Rashin, 1985 

[74] Zehfus MH, Rose GD. (1986). "Compact units in proteins". Biochemistry 25 (19): 5759-65. doi:10.1021/bi00367a062. PMID 3778881. 
[75] http://rigidfinder.molmovdb.org 
[76] http ://pisqrd. escience-lab. org 
[77] Potestio, R., Pontiggia, F. and Micheletti, C. (2009). "Coarse-grained description of protein internal dynamics: an optimal strategy for 

decomposing proteins in rigid subunits." (http://www.cell.com/biophysj/abstract/S0006- 3495(09)00781-4). Biophysical Journal 96 (12): 

4993-5002. doi:10.1016/j.bpj.2009.03.051. PMID 19527659. PMC 2712024. . 
[78] Aleksiev, T., Potestio, R., Pontiggia, F., Cozzini, S. and Micheletti, C. (2009). "PiSQRD: a web server for decomposing proteins into 

quasi-rigid dynamical domains." (http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btp512). Bioinformatics 25 (20): 2743-4. 

doi:10.1093/bioinformatics/btp512. PMID 19696046. . 
[79] Barclay A (2003). "Membrane proteins with immunoglobulin-like domains— a master superfamily of interaction molecules". Semin Immunol 

15 (4): 215-23. doi:10.1016/S1044-5323(03)00047-2. PMID 14690046. 
[80] http://www.compbio.dundee.ac.uk/3Dee/ 
[81] http://www.cathdb.info/ 

[82] http://ekhidna.biocenter.helsinki.fi/dali_server/ 
[83] http://scop.mrc-lmb.cam.ac.uk/scop 

[84] http://pawsonlab.mshri.on.ca/index.php?option=com_content&task=view&id=30&Itemid=63/ 
[85] http://nashlab.bsd. uchicago.edu/index. php?option=com_content&task=section&id=4&Itemid=29 
[86] http://realm.sdsc.edu/pdomains/ 
[87] http ://www. ebi. ac.uk/interpro 
[88] http://pfam.sanger.ac.uk/ 
[89] http://www.expasy.org/prosite/ 
[90] http://prodom.prabi.fr 
[91] http://SMART.embl-heidelberg.de 

[92] http ://www. ncbi.nlm. nih. go v: 80/S tructure/cdd/cdd. shtml 
[93] http://supfam.org/SUPERFAMILY 

[94] http://www.sanger.ac.Uk//Software/Pfam/browse/clans.shtml#159 
[95] http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=10592235 
[96] http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=l 1 125048 
[97] http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=10592241 
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[100] http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=l 1 125040 



Nucleic Acids 189 



Nucleic Acids 



A nucleic acid is a macromolecule composed of chains of monomeric nucleotides. In biochemistry these molecules 
carry genetic information or form structures within cells. The most common nucleic acids are deoxyribonucleic acid 
(DNA) and ribonucleic acid (RNA). Nucleic acids are universal in living things, as they are found in all cells and 
viruses. Nucleic acids were first discovered by Friedrich Miescher in 1871. 

Artificial nucleic acids include peptide nucleic acid (PNA), Morpholino and locked nucleic acid (LNA), as well as 
glycol nucleic acid (GNA) and threose nucleic acid (TNA). Each of these is distinguished from naturally-occurring 
DNA or RNA by changes to the backbone of the molecule. 

Chemical structure 

The term "nucleic acid" is the generic name for a family of biopolymers, named for their role in the cell nucleus. It 
was later discovered that some nucleic acids are exclusive of the mitochondrion (e.g. Mitochondrial DNA). The 
monomers from which nucleic acids are constructed are called nucleotides. Nucleic acids are linear, unbranched 
polymers of nucleotides. 

Each nucleotide consists of three components: a nitrogenous heterocyclic base, which is either a purine or a 
pyrimidine; a pentose sugar; and a phosphate group. Nucleic acid types differ in the structure of the sugar in their 
nucleotides - DNA contains 2-deoxyribose while RNA contains ribose (where the only difference is the presence of a 
hydroxyl group). Also, the nitrogenous bases found in the two nucleic acid types are different: adenine, cytosine, and 
guanine are found in both RNA and DNA, while thymine only occurs in DNA and uracil only occurs in RNA. Other 
rare nucleic acid bases can occur, for example inosine in strands of mature transfer RNA. 

Nucleic acids are usually either single-stranded or double-stranded, though structures with three or more strands can 
form. A double-stranded nucleic acid consists of two single-stranded nucleic acids held together by hydrogen bonds, 
such as in the DNA double helix. In contrast, RNA is usually single-stranded, but any given strand may fold back 
upon itself to form secondary structure as in tRNA and rRNA. Within cells, DNA is usually double-stranded, though 
some viruses have single-stranded DNA as their genome. Retroviruses have single-stranded RNA as their genome. 

The sugars and phosphates in nucleic acids are connected to each other in an alternating chain, linked by shared 
oxygens, forming a phosphodiester bond. In conventional nomenclature, the carbons to which the phosphate groups 
attach are the 3' end and the 5' end carbons of the sugar. This gives nucleic acids polarity. The bases extend from a 
glycosidic linkage to the 1' carbon of the pentose sugar ring. Bases are joined through N-l of pyrimidines and N-9 of 
purines to 1' carbon of ribose through N-p glycosyl bond. 

Types of nucleic acids 
Ribonucleic acid 

Ribonucleic acid, or RNA, is a nucleic acid polymer consisting of nucleotide monomers, which plays several 
important roles in the processes of transcribing genetic information from deoxyribonucleic acid (DNA) into proteins. 
RNA acts as a messenger between DNA and the protein synthesis complexes known as ribosomes, forms vital 
portions of ribosomes, and serves as an essential carrier molecule for amino acids to be used in protein synthesis. 
The three types of RNA include tRNA (transfer), mRNA (messenger) and rRNA (ribosomal). 



Nucleic Acids 190 

Deoxyribonucleic acid 

Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and 
functioning of all known living organisms. The main role of DNA molecules is the long-term storage of information 
and DNA is often compared to a set of blueprints, since it contains the instructions needed to construct other 
components of cells, such as proteins and RNA molecules. The DNA segments that carry this genetic information 
are called genes, but other DNA sequences have structural purposes, or are involved in regulating the use of this 
genetic information. 

DNA is made of four types of nucleotides, containing different nucleobases: the pyrimidines cytosine and thymine, 
and the purines guanine and adenine. The nucleotides are attached to each other in a chain by bonds between their 
sugar and phosphate groups, forming a sugar-phosphate backbone. Two of these chains are held together by 
hydrogen bonding between complementary bases; the chains coil around each other, forming the DNA double helix. 

Nucleic acid components 
Nucleobases 

Nucleobases are heterocyclic aromatic organic compounds containing nitrogen atoms. Nucleobases are the parts of 
RNA and DNA involved in base pairing. Cytosine, guanine, adenine, thymine are found predominantly in DNA, 
while in RNA uracil replaces thymine. These are abbreviated as C, G, A, T, U, respectively. 

Nucleobases are complementary, and when forming base pairs, must always join accordingly: cytosine-guanine, 
adenine-thymine (adenine-uracil when RNA). The strength of the interaction between cytosine and guanine is 
stronger than between adenine and thymine because the former pair has three hydrogen bonds joining them while the 
latter pair have only two. Thus, the higher the GC content of double-stranded DNA, the more stable the molecule 
and the higher the melting temperature. 

Two main nucleobase classes exist, named for the molecule which forms their skeleton. These are the double-ringed 
purines and single-ringed pyrimidines. Adenine and guanine are purines (abbreviated as R), while cytosine, thymine, 
and uracil are all pyrimidines (abbreviated as Y). 

Hypoxanthine and xanthine are mutant forms of adenine and guanine, respectively, created through mutagen 
presence, through deamination (replacement of the amine-group with a hydroxyl-group). These are abbreviated HX 
andX 

Nucleosides 

Nucleosides are glycosylamines made by attaching a nucleobase (often referred to simply as bases) to a ribose or 
deoxyribose (sugar) ring. In short, a nucleoside is a base linked to sugar. The names derive from the nucleobase 
names. The nucleosides commonly occurring in DNA and RNA include cytidine, uridine, adenosine, guanosine and 
thymidine. When a phosphate is added to a nucleoside (by phosphorylated by a specific kinase enzyme), a nucleotide 
is produced. Nucleoside analogues, such as acyclovir, are sometimes used as antiviral agents. 



Nucleic Acids 191 

Nucleotides and deoxynucleotides 

A nucleotide consists of a nucleoside and one phosphate group. Nucleotides are the monomers of RNA and DNA, as 
well as forming the structural units of several important cofactors - CoA, flavin adenine dinucleotide, flavin 
mononucleotide, adenosine triphosphate and nicotinamide adenine dinucleotide phosphate. In the cell nucleotides 
play important roles in metabolism, and signaling. 

Nucleotides are named after the nucleoside on which they are based, in conjunction with the number of phosphates 
they contain, for example: 

• Adenine bonded to ribose forms the nucleoside adenosine. 

• Adenosine bonded to a phosphate forms adenosine monophosphate. 

• As phosphates are added, adenosine diphosphate and adenosine triphosphate are formed, in sequence. 

See also 

• Nucleic acid methods 

• Nucleic acid simulations 

References 

• Wolfram Saenger, Principles of Nucleic Acid Structure, 1984, Springer- Verlag New York Inc. 

• Keith Roberts, Martin Raff, Bruce Alberts, Peter Walter, Julian Lewis and Alexander Johnson, Molecular Biology 
of the Cell 4th Edition, Routledge, March, 2002, hardcover, 1616 pages, 7.6 pounds, ISBN 0-8153-3218-1 

External links 

• Interview with Aaron Klug, Nobel Laureate for structural elucidation of biologically important nucleic-acid 
protein complexes provided by the Vega Science Trust. 

• Nucleic Acid Research Journal 

References 

[ 1 ] http : // w w w . vega. org. uk/ video/programme/ 122 
[2] http://nar.oxfordjournals.org/ 



DNA 



192 



DNA 



Deoxyribonucleic acid ( 43 /di'Dksl'ralboUnu'klilk 'aesld/ 
Wikipedia:Media helpFile:en-us-Deoxyribonucleic_acid.ogg) 

(DNA) is a nucleic acid that contains the genetic instructions used 
in the development and functioning of all known living organisms 
and some viruses. The main role of DNA molecules is the 
long-term storage of information. DNA is often compared to a set 
of blueprints or a recipe, or a code, since it contains the instructions 
needed to construct other components of cells, such as proteins and 
RNA molecules. The DNA segments that carry this genetic 
information are called genes, but other DNA sequences have 
structural purposes, or are involved in regulating the use of this 
genetic information. 

Chemically, DNA consists of two long polymers of simple units 
called nucleotides, with backbones made of sugars and phosphate 
groups joined by ester bonds. These two strands run in opposite 
directions to each other and are therefore anti-parallel. Attached to 
each sugar is one of four types of molecules called bases. It is the 
sequence of these four bases along the backbone that encodes 
information. This information is read using the genetic code, which 
specifies the sequence of the amino acids within proteins. The code 
is read by copying stretches of DNA into the related nucleic acid 
RNA, in a process called transcription. 




The structure of part of a DNA double helix 



Within cells, DNA is organized into long structures called chromosomes. These chromosomes are duplicated before 
cells divide, in a process called DNA replication. Eukaryotic organisms (animals, plants, fungi, and protists) store 
most of their DNA inside the cell nucleus and some of their DNA in organelles, such as mitochondria or 
chloroplasts. In contrast, prokaryotes (bacteria and archaea) store their DNA only in the cytoplasm. Within the 
chromosomes, chromatin proteins such as histones compact and organize DNA. These compact structures guide the 
interactions between DNA and other proteins, helping control which parts of the DNA are transcribed. 



DNA 



193 



Properties 

DNA is a long polymer made from 
repeating units called nucleotides. 



[4] 



The DNA chain 



is 22 to 
26 Angstroms wide (2.2 to 

2.6 nanometres), and one nucleotide unit 
is 3.3 A (0.33 nm) long. [5] Although each 
individual repeating unit is very small, 
DNA polymers can be very large 
molecules containing millions of 
nucleotides. For instance, the largest 
human chromosome, chromosome 
number 1, is approximately 220 million 



Adenine 



Thymine 



3' end 

OH 



base pairs long 



[6] 




backbone 



V- 

Cytosine /*"° 



Phosphate- 
deoxyribose"*)^ 

In living organisms, DNA does not 
usually exist as a single molecule, but 

instead as a pair of molecules that are 

T71 rsi 
held tightly together. These two 

long strands entwine like vines, in the 

shape of a double helix. The nucleotide 

repeats contain both the segment of the 

backbone of the molecule, which holds 

the chain together, and a base, which 

interacts with the other DNA strand in 

the helix. A base linked to a sugar is 

called a nucleoside and a base linked to a sugar and one or more phosphate groups is called a nucleotide. If multiple 

191 
nucleotides are linked together, as in DNA, this polymer is called a polynucleotide. 

The backbone of the DNA strand is made from alternating phosphate and sugar residues. The sugar in DNA is 
2-deoxyribose, which is a pentose (five-carbon) sugar. The sugars are joined together by phosphate groups that form 
phosphodiester bonds between the third and fifth carbon atoms of adjacent sugar rings. These asymmetric bonds 
mean a strand of DNA has a direction. In a double helix the direction of the nucleotides in one strand is opposite to 
their direction in the other strand: the strands are antiparallel. The asymmetric ends of DNA strands are called the 5' 
(five prime) and 3' (three prime) ends, with the 5' end having a terminal phosphate group and the 3' end a terminal 
hydroxyl group. One major difference between DNA and RNA is the sugar, with the 2-deoxyribose in DNA being 



Guanine 5e nd 

Chemical structure of DNA. Hydrogen bonds shown as dotted lines. 



replaced by the alternative pentose sugar ribose in RNA 



[8] 



DNA 



194 



The DNA double helix is stabilized by hydrogen bonds between 
the bases attached to the two strands. The four bases found in DNA 
are adenine (abbreviated A), cytosine (C), guanine (G) and thymine 
(T). These four bases are attached to the sugar/phosphate to form 
the complete nucleotide, as shown for adenosine monophosphate. 

These bases are classified into two types; adenine and guanine are 
fused five- and six-membered heterocyclic compounds called 
purines, while cytosine and thymine are six-membered rings called 

ro] 

pyrimidines. A fifth pyrimidine base, called uracil (U), usually 
takes the place of thymine in RNA and differs from thymine by 
lacking a methyl group on its ring. Uracil is not usually found in 
DNA, occurring only as a breakdown product of cytosine. In 
addition to RNA and DNA, a large number of artificial nucleic acid 
analogues have also been created to study the proprieties of nucleic 
acids, or for use in biotechnology. 

Grooves 

Twin helical strands form the DNA backbone. Another double 
helix may be found by tracing the spaces, or grooves, between the 
strands. These voids are adjacent to the base pairs and may provide 
a binding site. As the strands are not directly opposite each other, 
the grooves are unequally sized. One groove, the major groove, is 
22 A wide and the other, the minor groove, is 12 A wide. The 
narrowness of the minor groove means that the edges of the bases 
are more accessible in the major groove. As a result, proteins like 
transcription factors that can bind to specific sequences in double-stranded DNA usually make contacts to the sides 

ri4i 

of the bases exposed in the major groove. This situation varies in unusual conformations of DNA within the cell 
(see below), but the major and minor grooves are always named to reflect the differences in size that would be seen 
if the DNA is twisted back into the ordinary B form. 




A section of DNA. The bases lie horizontally between 

the two spiraling strands. Animated version at 

File:DNA orbit animated.gif. 



Base pairing 

Each type of base on one strand forms a bond with just one type of base on the other strand. This is called 
complementary base pairing. Here, purines form hydrogen bonds to pyrimidines, with A bonding only to T, and C 
bonding only to G. This arrangement of two nucleotides binding together across the double helix is called a base 
pair. As hydrogen bonds are not covalent, they can be broken and rejoined relatively easily. The two strands of DNA 
in a double helix can therefore be pulled apart like a zipper, either by a mechanical force or high temperature. As 
a result of this complementarity, all the information in the double-stranded sequence of a DNA helix is duplicated on 
each strand, which is vital in DNA replication. Indeed, this reversible and specific interaction between 
complementary base pairs is critical for all the functions of DNA in living organisms. 



DNA 195 




H 
,0 

H 0, 



n 
H H H 



w v :» ^ -> > 



-H-- i ) L N ' h 



r\ 



Guanine H Cytosine 

Adenine Thymine 

Top, a GC base pair with three hydrogen bonds. Bottom, an AT base pair with two hydrogen bonds. Non-covalent 

hydrogen bonds between the pairs are shown as dashed lines. 

The two types of base pairs form different numbers of hydrogen bonds, AT forming two hydrogen bonds, and GC 
forming three hydrogen bonds (see figures, left). DNA with high GC-content is more stable than DNA with low 
GC-content, but contrary to popular belief, this is not due to the extra hydrogen bond of a GC base pair but rather the 
contribution of stacking interactions (hydrogen bonding merely provides specificity of the pairing, not stability). 
As a result, it is both the percentage of GC base pairs and the overall length of a DNA double helix that determine 
the strength of the association between the two strands of DNA. Long DNA helices with a high GC content have 

ri7i 

stronger-interacting strands, while short helices with high AT content have weaker-interacting strands. In biology, 
parts of the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in some promoters, 
tend to have a high AT content, making the strands easier to pull apart. In the laboratory, the strength of this 
interaction can be measured by finding the temperature required to break the hydrogen bonds, their melting 
temperature (also called T value). When all the base pairs in a DNA double helix melt, the strands separate and 
exist in solution as two entirely independent molecules. These single-stranded DNA molecules have no single 

ri9i 

common shape, but some conformations are more stable than others. 

Sense and antisense 

A DNA sequence is called "sense" if its sequence is the same as that of a messenger RNA copy that is translated into 
protein. The sequence on the opposite strand is called the "antisense" sequence. Both sense and antisense 
sequences can exist on different parts of the same strand of DNA (i.e. both strands contain both sense and antisense 
sequences). In both prokaryotes and eukaryotes, antisense RNA sequences are produced, but the functions of these 
RNAs are not entirely clear. One proposal is that antisense RNAs are involved in regulating gene expression 

To?! 

through RNA-RNA base pairing. 

A few DNA sequences in prokaryotes and eukaryotes, and more in plasmids and viruses, blur the distinction between 
sense and antisense strands by having overlapping genes. In these cases, some DNA sequences do double duty, 

encoding one protein when read along one strand, and a second protein when read in the opposite direction along the 

T241 
other strand. In bacteria, this overlap may be involved in the regulation of gene transcription, while in viruses, 

[25] 
overlapping genes increase the amount of information that can be encoded within the small viral genome. 

Supercoiling 

DNA can be twisted like a rope in a process called DNA supercoiling. With DNA in its "relaxed" state, a strand 

usually circles the axis of the double helix once every 10.4 base pairs, but if the DNA is twisted the strands become 

more tightly or more loosely wound. If the DNA is twisted in the direction of the helix, this is positive 

supercoiling, and the bases are held more tightly together. If they are twisted in the opposite direction, this is 

negative supercoiling, and the bases come apart more easily. In nature, most DNA has slight negative supercoiling 

[271 
that is introduced by enzymes called topoisomerases. These enzymes are also needed to relieve the twisting 



DNA 



196 



stresses introduced into DNA strands during processes such as transcription and DNA replication 



1 28 1 



Alternate DNA structures 

DNA exists in many possible conformations 
that include A-DNA, B-DNA, and Z-DNA 
forms, although, only B-DNA and Z-DNA 
have been directly observed in functional 
organisms. The conformation that DNA 
adopts depends on the hydration level, DNA 
sequence, the amount and direction of 
supercoiling, chemical modifications of the 
bases, the type and concentration of metal 
ions, as well as the presence of polyamines in 



solution 



[29] 




The first published reports of A-DNA X-ray 

diffraction patterns — and also B-DNA used analyses based on Patterson transforms that provided only a limited 
amount of structural information for oriented fibers of DNA. An alternate analysis was then proposed by 

Wilkins et al, in 1953, for the in vivo B-DNA X-ray diffraction/scattering patterns of highly hydrated DNA fibers in 

F321 

terms of squares of Bessel functions. In the same journal, Watson and Crick presented their molecular modeling 

T71 
analysis of the DNA X-ray diffraction patterns to suggest that the structure was a double-helix. 

T331 
Although the "B-DNA form' is most common under the conditions found in cells, it is not a well-defined 

T341 
conformation but a family of related DNA conformations that occur at the high hydration levels present in living 

cells. Their corresponding X-ray diffraction and scattering patterns are characteristic of molecular paracrystals with a 

significant degree of disorder. 

Compared to B-DNA, the A-DNA form is a wider right-handed spiral, with a shallow, wide minor groove and a 
narrower, deeper major groove. The A form occurs under non-physiological conditions in partially dehydrated 
samples of DNA, while in the cell it may be produced in hybrid pairings of DNA and RNA strands, as well as in 

T371 T3R1 

enzyme-DNA complexes. Segments of DNA where the bases have been chemically modified by methylation 

may undergo a larger change in conformation and adopt the Z form. Here, the strands turn about the helical axis in a 

[391 
left-handed spiral, the opposite of the more common B form. These unusual structures can be recognized by 

specific Z-DNA binding proteins and may be involved in the regulation of transcription 



[40] 



DNA 



197 




Quadruplex structures 

At the ends of the linear chromosomes are 

specialized regions of DNA called telomeres. The 

main function of these regions is to allow the cell to 

replicate chromosome ends using the enzyme 

telomerase, as the enzymes that normally replicate 

DNA cannot copy the extreme 3' ends of 

chromosomes. These specialized chromosome 

caps also help protect the DNA ends, and stop the 

DNA repair systems in the cell from treating them as 

[43] 
damage to be corrected. In human cells, telomeres 

are usually lengths of single-stranded DNA 

containing several thousand repeats of a simple 



TTAGGG sequence. 



[44] 



DNA quadruplex formed by telomere repeats. The looped conformation 

[41] 
of the DNA backbone is very different from the typical DNA helix. 



These guanine-rich sequences may stabilize 
chromosome ends by forming structures of stacked 
sets of four-base units, rather than the usual base 

pairs found in other DNA molecules. Here, four guanine bases form a flat plate and these flat four-base units then 

1451 
stack on top of each other, to form a stable G-quadruplex structure. These structures are stabilized by hydrogen 

bonding between the edges of the bases and chelation of a metal ion in the centre of each four-base unit. Other 

structures can also be formed, with the central set of four bases coming from either a single strand folded around the 

bases, or several different parallel strands, each contributing one base to the central structure. 

In addition to these stacked structures, telomeres also form large loop structures called telomere loops, or T-loops. 
Here, the single-stranded DNA curls around in a long circle stabilized by telomere-binding proteins. At the very 
end of the T-loop, the single-stranded telomere DNA is held onto a region of double-stranded DNA by the telomere 
strand disrupting the double-helical DNA and base pairing to one of the two strands. This triple-stranded structure is 
called a displacement loop or D-loop 



[45] 



< 



Single branch Multiple branches 




Branched DNA can form networks containing multiple branches. 



Branched DNA 

In DNA fraying occurs when non-complementary regions exist at the end of an otherwise complementary 
double-strand of DNA. However, branched DNA can occur if a third strand of DNA is introduced and contains 
adjoining regions able to hybridize with the frayed regions of the pre-existing double-strand. Although the simplest 
example of branched DNA involves only three strands of DNA, complexes involving additional strands and multiple 
branches are also possible. Branched DNA can be used in nanotechnology to construct geometric shapes, see the 
section on uses in technology below. 



DNA 



198 



Chemical modifications 



NH 2 
N 

H 



cytosine 5-methylcytosine 





thymine 



Structure of cytosine with and without the 5-methyl group. Deamination converts 5-methylcytosine into thymine. 



Base modifications 

The expression of genes is influenced by how the DNA is packaged in chromosomes, in a structure called chromatin. 
Base modifications can be involved in packaging, with regions that have low or no gene expression usually 
containing high levels of methylation of cytosine bases. For example, cytosine methylation, produces 
5-methylcytosine, which is important for X-chromosome inactivation. The average level of methylation varies 
between organisms - the worm Caenorhabditis elegans lacks cytosine methylation, while vertebrates have higher 
levels, with up to 1% of their DNA containing 5-methylcytosine. Despite the importance of 5-methylcytosine, it 
can deaminate to leave a thymine base, methylated cytosines are therefore particularly prone to mutations. Other 

T52] 

base modifications include adenine methylation in bacteria, the presence of 5-hydroxymethylcytosine in the brain, 



and the glycosylation of uracil to produce the "J-base" in kinetoplastids 



[53] [54] 



Damage 

DNA can be damaged by many sorts of mutagens, 
which change the DNA sequence. Mutagens include 
oxidizing agents, alkylating agents and also 
high-energy electromagnetic radiation such as 
ultraviolet light and X-rays. The type of DNA damage 
produced depends on the type of mutagen. For 
example, UV light can damage DNA by producing 
thymine dimers, which are cross-links between 
pyrimidine bases. On the other hand, oxidants such 
as free radicals or hydrogen peroxide produce multiple 
forms of damage, including base modifications, 

[57] 

particularly of guanosine, and double-strand breaks. 
A typical human cell contains about 150,000 bases that 

rcoi 

have suffered oxidative damage. Of these oxidative 
lesions, the most dangerous are double-strand breaks, 
as these are difficult to repair and can produce point 
mutations, insertions and deletions from the DNA 



sequence, as well as chromosomal translocations 



[59] 



Many mutagens fit into the space between two adjacent 
base pairs, this is called intercalating. Most 
intercalators are aromatic and planar molecules, and 
include Ethidium bromide, daunomycin, and 




A covalent adduct between benzo[a]pyrene, the major mutagen in 
tobacco smoke, and DNA 



DNA 199 

doxorubicin. In order for an intercalator to fit between base pairs, the bases must separate, distorting the DNA 
strands by unwinding of the double helix. This inhibits both transcription and DNA replication, causing toxicity and 
mutations. As a result, DNA intercalators are often carcinogens, and Benzo[a]pyrene diol epoxide, acridines, 
aflatoxin and ethidium bromide are well-known examples. Nevertheless, due to their ability to inhibit 

DNA transcription and replication, other similar toxins are also used in chemotherapy to inhibit rapidly growing 
cancer cells. 

Biological functions 

DNA usually occurs as linear chromosomes in eukaryotes, and circular chromosomes in prokaryotes. The set of 
chromosomes in a cell makes up its genome; the human genome has approximately 3 billion base pairs of DNA 
arranged into 46 chromosomes. The information carried by DNA is held in the sequence of pieces of DNA called 
genes. Transmission of genetic information in genes is achieved via complementary base pairing. For example, in 
transcription, when a cell uses the information in a gene, the DNA sequence is copied into a complementary RNA 
sequence through the attraction between the DNA and the correct RNA nucleotides. Usually, this RNA copy is then 
used to make a matching protein sequence in a process called translation which depends on the same interaction 
between RNA nucleotides. Alternatively, a cell may simply copy its genetic information in a process called DNA 
replication. The details of these functions are covered in other articles; here we focus on the interactions between 
DNA and other molecules that mediate the function of the genome. 

Genes and genomes 

Genomic DNA is located in the cell nucleus of eukaryotes, as well as small amounts in mitochondria and 
chloroplasts. In prokaryotes, the DNA is held within an irregularly shaped body in the cytoplasm called the 
nucleoid. The genetic information in a genome is held within genes, and the complete set of this information in an 
organism is called its genotype. A gene is a unit of heredity and is a region of DNA that influences a particular 
characteristic in an organism. Genes contain an open reading frame that can be transcribed, as well as regulatory 
sequences such as promoters and enhancers, which control the transcription of the open reading frame. 

In many species, only a small fraction of the total sequence of the genome encodes protein. For example, only about 
1.5% of the human genome consists of protein-coding exons, with over 50% of human DNA consisting of 
non-coding repetitive sequences. The reasons for the presence of so much non-coding DNA in eukaryotic 
genomes and the extraordinary differences in genome size, or C-value, among species represent a long-standing 
puzzle known as the "C-value enigma." However, DNA sequences that do not code protein may still encode 
functional non-coding RNA molecules, which are involved in the regulation of gene expression. 



DNA 



200 




T7 RNA polymerase (blue) producing a mRNA (green) from a DNA template 
(orange). 



Some non-coding DNA sequences play 
structural roles in chromosomes. Telomeres 
and centromeres typically contain few 
genes, but are important for the function and 
stability of chromosomes. An 

abundant form of non-coding DNA in 
humans are pseudogenes, which are copies 
of genes that have been disabled by 
mutation. These sequences are usually 
just molecular fossils, although they can 
occasionally serve as raw genetic material 
for the creation of new genes through the 
process of gene duplication and 
divergence 



[72] 



Transcription and translation 



A gene is a sequence of DNA that contains genetic information and can influence the phenotype of an organism. 
Within a gene, the sequence of bases along a DNA strand defines a messenger RNA sequence, which then defines 
one or more protein sequences. The relationship between the nucleotide sequences of genes and the amino-acid 
sequences of proteins is determined by the rules of translation, known collectively as the genetic code. The genetic 
code consists of three-letter 'words' called codons formed from a sequence of three nucleotides (e.g. ACT, CAG, 
TTT). 

In transcription, the codons of a gene are copied into messenger RNA by RNA polymerase. This RNA copy is then 
decoded by a ribosome that reads the RNA sequence by base-pairing the messenger RNA to transfer RNA, which 
carries amino acids. Since there are 4 bases in 3-letter combinations, there are 64 possible codons ( ^ 3 
combinations). These encode the twenty standard amino acids, giving most amino acids more than one possible 
codon. There are also three 'stop' or 'nonsense' codons signifying the end of the coding region; these are the TAA, 
TGA and TAG codons. 



Replication 

Cell division is essential for an 
organism to grow, but when a cell 
divides it must replicate the DNA in its 
genome so that the two daughter cells 
have the same genetic information as 
their parent. The double-stranded 
structure of DNA provides a simple 
mechanism for DNA replication. Here, 
the two strands are separated and then 
each strand's complementary DNA 
sequence is recreated by an enzyme 
called DNA polymerase. This enzyme 
makes the complementary strand by 



DNA ligase 
DNA Polymerase (Pola) 




Leading 
strand 



Topoisomerase 



DNA Polymerase (PolS) ' 

Helitase' 
Single strand. 
Binding proteins 

DNA replication. The double helix is unwound by a helicase and topoisomerase. Next, 

one DNA polymerase produces the leading strand copy. Another DNA polymerase binds 

to the lagging strand. This enzyme makes discontinuous segments (called Okazaki 

fragments) before DNA ligase joins them together. 



finding the correct base through complementary base pairing, and bonding it onto the original strand. As DNA 
polymerases can only extend a DNA strand in a 5' to 3' direction, different mechanisms are used to copy the 



DNA 



201 



T731 
antiparallel strands of the double helix. In this way, the base on the old strand dictates which base appears on the 

new strand, and the cell ends up with a perfect copy of its DNA. 

Interactions with proteins 

All the functions of DNA depend on interactions with proteins. These protein interactions can be non-specific, or the 
protein can bind specifically to a single DNA sequence. Enzymes can also bind to DNA and of these, the 
polymerases that copy the DNA base sequence in transcription and DNA replication are particularly important. 



DNA-binding proteins 




Interaction of DNA with histones (shown in white, top). These proteins' basic amino acids (below left, blue) bind to 
the acidic phosphate groups on DNA (below right, red). 

Structural proteins that bind DNA are well-understood examples of non-specific DNA-protein interactions. Within 
chromosomes, DNA is held in complexes with structural proteins. These proteins organize the DNA into a compact 
structure called chromatin. In eukaryotes this structure involves DNA binding to a complex of small basic proteins 

[741 [751 

called histones, while in prokaryotes multiple types of proteins are involved. The histones form a disk-shaped 

complex called a nucleosome, which contains two complete turns of double-stranded DNA wrapped around its 
surface. These non-specific interactions are formed through basic residues in the histones making ionic bonds to the 
acidic sugar-phosphate backbone of the DNA, and are therefore largely independent of the base sequence 



[76] 
[77] 



Chemical modifications of these basic amino acid residues include methylation, phosphorylation and acetylation. 
These chemical changes alter the strength of the interaction between the DNA and the histones, making the DNA 

[7R] 

more or less accessible to transcription factors and changing the rate of transcription. Other non-specific 

DNA-binding proteins in chromatin include the high-mobility group proteins, which bind to bent or distorted 

[79] 
DNA. These proteins are important in bending arrays of nucleosomes and arranging them into the larger 

structures that make up chromosomes. 

A distinct group of DNA-binding proteins are the DNA-binding proteins that specifically bind single-stranded DNA. 
In humans, replication protein A is the best-understood member of this family and is used in processes where the 

[SI] 

double helix is separated, including DNA replication, recombination and DNA repair. These binding proteins 
seem to stabilize single-stranded DNA and protect it from forming stem-loops or being degraded by nucleases. 



DNA 



202 



In contrast, other proteins have evolved to bind to particular DNA 
sequences. The most intensively studied of these are the various 
transcription factors, which are proteins that regulate transcription. 
Each transcription factor binds to one particular set of DNA 
sequences and activates or inhibits the transcription of genes that have 
these sequences close to their promoters. The transcription factors do 
this in two ways. Firstly, they can bind the RNA polymerase 
responsible for transcription, either directly or through other mediator 
proteins; this locates the polymerase at the promoter and allows it to 
begin transcription. Alternatively, transcription factors can bind 
enzymes that modify the histones at the promoter; this will change the 
accessibility of the DNA template to the polymerase 



[84] 




As these DNA targets can occur throughout an organism's genome, 
changes in the activity of one type of transcription factor can affect 

roc] 

thousands of genes. Consequently, these proteins are often the 

targets of the signal transduction processes that control responses to 

environmental changes or cellular differentiation and development. 

The specificity of these transcription factors' interactions with DNA 

come from the proteins making multiple contacts to the edges of the 

DNA bases, allowing them to "read" the DNA sequence. Most of these base-interactions are made in the major 

groove, where the bases are most accessible. 



The lambda repressor helix-turn-helix transcription 

T821 
factor bound to its DNA target 




The restriction enzyme EcoRV (green) in a complex with its substrate 

DNA [87] 



DNA-modifying enzymes 

Nucleases and ligases 

Nucleases are enzymes that cut DNA strands by 
catalyzing the hydrolysis of the phosphodiester bonds. 
Nucleases that hydrolyse nucleotides from the ends of 
DNA strands are called exonucleases, while 
endonucleases cut within strands. The most frequently 
used nucleases in molecular biology are the restriction 
endonucleases, which cut DNA at specific sequences. 
For instance, the EcoRV enzyme shown to the left 
recognizes the 6-base sequence 5'-GATIATC-3' and 
makes a cut at the vertical line. In nature, these 
enzymes protect bacteria against phage infection by 



[88] 



In 



digesting the phage DNA when it enters the bacterial cell, acting as part of the restriction modification system 
technology, these sequence-specific nucleases are used in molecular cloning and DNA fingerprinting. 

Enzymes called DNA ligases can rejoin cut or broken DNA strands. Ligases are particularly important in lagging 
strand DNA replication, as they join together the short segments of DNA produced at the replication fork into a 
complete copy of the DNA template. They are also used in DNA repair and genetic recombination. 



DNA 203 

Topoisomerases and helicases 

Topoisomerases are enzymes with both nuclease and ligase activity. These proteins change the amount of 

supercoiling in DNA. Some of these enzymes work by cutting the DNA helix and allowing one section to rotate, 

T271 
thereby reducing its level of supercoiling; the enzyme then seals the DNA break. Other types of these enzymes 

are capable of cutting one DNA helix and then passing a second strand of DNA through this break, before rejoining 

the helix. Topoisomerases are required for many processes involving DNA, such as DNA replication and 

• ♦■ [28] 
transcription. 

Helicases are proteins that are a type of molecular motor. They use the chemical energy in nucleoside triphosphates, 
predominantly ATP, to break hydrogen bonds between bases and unwind the DNA double helix into single 
strands. These enzymes are essential for most processes where enzymes need to access the DNA bases. 

Polymerases 

Polymerases are enzymes that synthesize polynucleotide chains from nucleoside triphosphates. The sequence of their 
products are copies of existing polynucleotide chains - which are called templates. These enzymes function by 
adding nucleotides onto the 3' hydroxyl group of the previous nucleotide in a DNA strand. Consequently, all 
polymerases work in a 5' to 3' direction. In the active site of these enzymes, the incoming nucleoside triphosphate 
base-pairs to the template: this allows polymerases to accurately synthesize the complementary strand of their 
template. Polymerases are classified according to the type of template that they use. 

In DNA replication, a DNA-dependent DNA polymerase makes a copy of a DNA sequence. Accuracy is vital in this 

process, so many of these polymerases have a proofreading activity. Here, the polymerase recognizes the occasional 

mistakes in the synthesis reaction by the lack of base pairing between the mismatched nucleotides. If a mismatch is 

detected, a 3' to 5' exonuclease activity is activated and the incorrect base removed. In most organisms DNA 

polymerases function in a large complex called the replisome that contains multiple accessory subunits, such as the 

[941 
DNA clamp or helicases. 

RNA-dependent DNA polymerases are a specialized class of polymerases that copy the sequence of an RNA strand 
into DNA. They include reverse transcriptase, which is a viral enzyme involved in the infection of cells by 

[42] [95] 

retroviruses, and telomerase, which is required for the replication of telomeres. Telomerase is an unusual 

T431 
polymerase because it contains its own RNA template as part of its structure. 

Transcription is carried out by a DNA-dependent RNA polymerase that copies the sequence of a DNA strand into 
RNA. To begin transcribing a gene, the RNA polymerase binds to a sequence of DNA called a promoter and 
separates the DNA strands. It then copies the gene sequence into a messenger RNA transcript until it reaches a 
region of DNA called the terminator, where it halts and detaches from the DNA. As with human DNA-dependent 
DNA polymerases, RNA polymerase II, the enzyme that transcribes most of the genes in the human genome, 
operates as part of a large protein complex with multiple regulatory and accessory subunits. 



DNA 



204 



Genetic recombination 




Structure of the Holliday junction intermediate in genetic recombination. The four separate DNA strands are 



[97] 



coloured red, blue, green and yellow 



M 



-HHI}- 



-[U — H} 



C2 

Recombination involves the breakage and rejoining of two 

chromosomes (M and F) to produce two re-arranged chromosomes 

(CI and C2). 



A DNA helix usually does not interact with other 
segments of DNA, and in human cells the different 
chromosomes even occupy separate areas in the 
nucleus called "chromosome territories". This 

physical separation of different chromosomes is 
important for the ability of DNA to function as a stable 
repository for information, as one of the few times 
chromosomes interact is during chromosomal crossover 
when they recombine. Chromosomal crossover is when 
two DNA helices break, swap a section and then rejoin. 

Recombination allows chromosomes to exchange 
genetic information and produces new combinations of 
genes, which increases the efficiency of natural 
selection and can be important in the rapid evolution of 



[99] 



new proteins. Genetic recombination can also be involved in DNA repair, particularly in the cell's response to 



double-strand breaks 



[100] 



The most common form of chromosomal crossover is homologous recombination, where the two chromosomes 
involved share very similar sequences. Non-homologous recombination can be damaging to cells, as it can produce 
chromosomal translocations and genetic abnormalities. The recombination reaction is catalyzed by enzymes known 
as recombinases, such as RAD51. The first step in recombination is a double-stranded break either caused by an 
endonuclease or damage to the DNA. A series of steps catalyzed in part by the recombinase then leads to joining 
of the two helices by at least one Holliday junction, in which a segment of a single strand in each helix is annealed to 
the complementary strand in the other helix. The Holliday junction is a tetrahedral junction structure that can be 
moved along the pair of chromosomes, swapping one strand for another. The recombination reaction is then halted 
by cleavage of the junction and re-ligation of the released DNA. 



DNA 205 

Evolution 

DNA contains the genetic information that allows all modern living things to function, grow and reproduce. 
However, it is unclear how long in the 4-billion-year history of life DNA has performed this function, as it has been 

[92] [1041 

proposed that the earliest forms of life may have used RNA as their genetic material. RNA may have acted 

as the central part of early cell metabolism as it can both transmit genetic information and carry out catalysis as part 
of ribozymes. This ancient RNA world where nucleic acid would have been used for both catalysis and genetics 
may have influenced the evolution of the current genetic code based on four nucleotide bases. This would occur 
since the number of different bases in such an organism is a trade-off between a small number of bases increasing 
replication accuracy and a large number of bases increasing the catalytic efficiency of ribozymes. 

Unfortunately, there is no direct evidence of ancient genetic systems, as recovery of DNA from most fossils is 
impossible. This is because DNA will survive in the environment for less than one million years and slowly degrades 
into short fragments in solution. Claims for older DNA have been made, most notably a report of the isolation of 
a viable bacterium from a salt crystal 250 million years old, but these claims are controversial. 

Uses in technology 
Genetic engineering 

Methods have been developed to purify DNA from organisms, such as phenol-chloroform extraction and manipulate 
it in the laboratory, such as restriction digests and the polymerase chain reaction. Modern biology and biochemistry 
make intensive use of these techniques in recombinant DNA technology. Recombinant DNA is a man-made DNA 
sequence that has been assembled from other DNA sequences. They can be transformed into organisms in the form 
of plasmids or in the appropriate format, by using a viral vector. The genetically modified organisms produced 
can be used to produce products such as recombinant proteins, used in medical research, or be grown in 

. .. [113] [114] 

agriculture. 

Forensics 

Forensic scientists can use DNA in blood, semen, skin, saliva or hair found at a crime scene to identify a matching 
DNA of an individual, such as a perpetrator. This process is called genetic fingerprinting, or more accurately, DNA 
profiling. In DNA profiling, the lengths of variable sections of repetitive DNA, such as short tandem repeats and 
minisatellites, are compared between people. This method is usually an extremely reliable technique for identifying a 
matching DNA. However, identification can be complicated if the scene is contaminated with DNA from several 
people. DNA profiling was developed in 1984 by British geneticist Sir Alec Jeffreys, and first used in 

forensic science to convict Colin Pitchfork in the 1988 Enderby murders case. 

People convicted of certain types of crimes may be required to provide a sample of DNA for a database. This has 
helped investigators solve old cases where only a DNA sample was obtained from the scene. DNA profiling can also 
be used to identify victims of mass casualty incidents. On the other hand, many convicted people have been 
released from prison on the basis of DNA techniques, which were not available when a crime had originally been 
committed. 

Bioinformatics 

Bioinformatics involves the manipulation, searching, and data mining of DNA sequence data. The development of 
techniques to store and search DNA sequences have led to widely applied advances in computer science, especially 
string searching algorithms, machine learning and database theory. String searching or matching algorithms, 

which find an occurrence of a sequence of letters inside a larger sequence of letters, were developed to search for 
specific sequences of nucleotides. In other applications such as text editors, even simple algorithms for this 



DNA 



206 



problem usually suffice, but DNA sequences cause these algorithms to exhibit near-worst-case behaviour due to their 
small number of distinct characters. The related problem of sequence alignment aims to identify homologous 
sequences and locate the specific mutations that make them distinct. These techniques, especially multiple sequence 

ri22i 

alignment, are used in studying phylogenetic relationships and protein function. Data sets representing entire 
genomes' worth of DNA sequences, such as those produced by the Human Genome Project, are difficult to use 
without annotations, which label the locations of genes and regulatory elements on each chromosome. Regions of 
DNA sequence that have the characteristic patterns associated with protein- or RNA-coding genes can be identified 
by gene finding algorithms, which allow researchers to predict the presence of particular gene products in an 

ri 231 

organism even before they have been isolated experimentally. 



DNA nanotechnology 

DNA nanotechnology uses the unique 
molecular recognition properties of 
DNA and other nucleic acids to create 
self-assembling branched DNA 
complexes with useful properties. 
DNA is thus used as a structural 
material rather than as a carrier of 
biological information. This has led to 
the creation of two-dimensional 
periodic lattices (both tile-based as 
well as using the "DNA origami" 
method) as well as three-dimensional 
structures in the shapes of 
polyhedra. Nanomechanical 

devices and algorithmic self-assembly 




The DNA structure at left (schematic shown) will self-assemble into the structure 

visualized by atomic force microscopy at right. DNA nanotechnology is the field which 

seeks to design nanoscale structures using the molecular recognition properties of DNA 

molecules. Image from Strong, 2004 (doi: 10. 1371/journal.pbio. 0020073). 



have also been demonstrated, and 

these DNA structures have been used to template the arrangement of other molecules such as gold nanoparticles and 

strep tavidin proteins . 



History and anthropology 

Because DNA collects mutations over time, which are then inherited, it contains historical information and by 

n 2si 
comparing DNA sequences, geneticists can infer the evolutionary history of organisms, their phylogeny. This 

field of phylogenetics is a powerful tool in evolutionary biology. If DNA sequences within a species are compared, 

population geneticists can learn the history of particular populations. This can be used in studies ranging from 

ecological genetics to anthropology; for example, DNA evidence is being used to try to identify the Ten Lost Tribes 

oflsrael. [129][130] 

DNA has also been used to look at modern family relationships, such as establishing family relationships between 
the descendants of Sally Hemings and Thomas Jefferson. This usage is closely related to the use of DNA in criminal 
investigations detailed above. Indeed, some criminal investigations have been solved when DNA from crime scenes 
has matched relatives of the guilty individual. 



DNA 



207 



History of DNA research 

DNA was first isolated by the Swiss physician Friedrich Miescher who, in 1869, discovered a microscopic substance 

ri32i 
in the pus of discarded surgical bandages. As it resided in the nuclei of cells, he called it "nuclein". In 1919, 

r 1331 

Phoebus Levene identified the base, sugar and phosphate nucleotide unit. Levene suggested that DNA consisted 
of a string of nucleotide units linked together through the phosphate groups. However, Levene thought the chain was 
short and the bases repeated in a fixed order. In 1937 William Astbury produced the first X-ray diffraction patterns 
that showed that DNA had a regular structure 



[134] 



In 1928, Frederick Griffith discovered that traits of the "smooth" form of the Pneumococcus could be transferred to 
the "rough" form of the same bacteria by mixing killed "smooth" bacteria with the live "rough" form. This 
system provided the first clear suggestion that DNA carried genetic information — the Avery-MacLeod-McCarty 
experiment — when Oswald Avery, along with coworkers Colin MacLeod and Maclyn McCarty, identified DNA as 
the transforming principle in 1943. DNA's role in heredity was confirmed in 1952, when Alfred Hershey and 



Martha Chase in the Hershey-Chase experiment showed that DNA is the genetic material of the T2 phage 



[137] 




DNA 



208 




Rosalind Franklin 




In 1953 James D. Watson and Francis Crick suggested what is now accepted as the first correct double-helix model 
of DNA structure in the journal Nature. Their double-helix, molecular model of DNA was then based on a single 

ri loi 

X-ray diffraction image (labeled as "Photo 51") " taken by Rosalind Franklin and Raymond Gosling in May 1952, 
as well as the information that the DNA bases were paired — also obtained through private communications from 
Erwin Chargaff in the previous years. Chargaff s rules played a very important role in establishing double-helix 
configurations for B-DNA as well as A-DNA. 

Experimental evidence supporting the Watson and Crick model were published in a series of five articles in the same 

ri 39i 

issue of Nature. Of these, Franklin and Gosling's paper was the first publication of their own X-ray diffraction 
data and original analysis method that partially supported the Watson and Crick model ; this issue also 

contained an article on DNA structure by Maurice Wilkins and two of his colleagues, whose analysis and in vivo 

B-DNA X-ray patterns also supported the presence in vivo of the double-helical DNA configurations as proposed by 

T321 
Crick and Watson for their double-helix molecular model of DNA in the previous two pages of Nature. In 1962, 

after Franklin's death, Watson, Crick, and Wilkins jointly received the Nobel Prize in Physiology or Medicine. 

Unfortunately, Nobel rules of the time allowed only living recipients, but a vigorous debate continues on who should 



receive credit for the discovery 



[142] 



DNA 209 

In an influential presentation in 1957, Crick laid out the "Central Dogma" of molecular biology, which foretold the 
relationship between DNA, RNA, and proteins, and articulated the "adaptor hypothesis". Final confirmation of 
the replication mechanism that was implied by the double-helical structure followed in 1958 through the 

ri44i 

Meselson-Stahl experiment. Further work by Crick and coworkers showed that the genetic code was based on 
non-overlapping triplets of bases, called codons, allowing Har Gobind Khorana, Robert W. Holley and Marshall 
Warren Nirenberg to decipher the genetic code. These findings represent the birth of molecular biology. 

See also 

Crystallography 

DNA microarray 

DNA sequencing 

Genetic disorder 

Junk DNA 

Molecular models of DNA 

Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid 

Nucleic acid analogues 

Nucleic acid methods 

Nucleic acid modeling 

Nucleic Acid Notations 

Paracrystal model and theory 

X-ray crystallography 

X-ray scattering 

Phosphoramidite 

Plasmid 

Polymerase chain reaction 

Proteopedia DNA [146] 

Southern blot 

Triple-stranded DNA 

Further reading 

• Calladine, Chris R.; Drew, Horace R.; Luisi, Ben F. and Travers, Andrew A. (2003). Understanding DNA: the 
molecule & how it works. Amsterdam: Elsevier Academic Press. ISBN 0-12-155089-3. 

• Dennis, Carina; Julie Clayton (2003). 50 years of DNA. Basingstoke: Palgrave Macmillan. ISBN 1-4039-1479-6. 

• Judson, Horace Freeland (1996). The eighth day of creation: makers of the revolution in biology. Plainview, N.Y: 
CSHL Press. ISBN 0-87969-478-5. 

• Olby, Robert C. (1994). The path to the double helix: the discovery of DNA. New York: Dover Publications. 
ISBN 0-486-681 17-3., first published in October 1974 by MacMillan, with foreword by Francis Crick;the 
definitive DNA textbook,revised in 1994 with a 9 page postscript. 

• Olby, Robert C. (2009). Francis Crick: A Biography. Plainview, N.Y: Cold Spring Harbor Laboratory Press. 
ISBN 0-87969-798-9. 

• Ridley, Matt (2006). Francis Crick: discoverer of the genetic code. [Ashland, OH: Eminent Lives, Atlas Books. 
ISBN 0-06-082333-X. 

• Berry, Andrew; Watson, James D. (2003). DNA: the secret of life. New York: Alfred A. Knopf. 
ISBN 0-375-41546-7. 

• Stent, Gunther Siegmund; Watson, James D. (1980). The double helix: a personal account of the discovery of the 
structure of DNA. New York: Norton. ISBN 0-393-95075-1. 



DNA 210 

• Wilkins, Maurice (2003). The third man of the double helix the autobiography of Maurice Wilkins. Cambridge, 
Eng: University Press. ISBN 0-19-860665-6. 

External links 

DNA at the Open Directory Project 

DNA binding site prediction on protein 



DNA from the Beginning Another DNA Learning Center site on DNA, genes, and heredity from Mendel to 

DNA Lab, demonstrates how to extract DNA from wheat using readily available equipment and supplies. 

52] Fr 
DNA under electron microscope 

Double Helix: 50 years of DNA [155] , Nature 



DNA coiling to form chromosomes 
DNA from the Beginning 
the human genome project. 
DNA Lab, demonstrates ho 

DNA the Double Helix Game From the official Nobel Prize web site 

DNA under electron microscope 
Dolan DNA Learning Center 
Double Helix: 50 years of DNA [lt 

Double Helix 1953—2003 National Centre for Biotechnology Education 

Francis Crick and James Watson talking on the BBC in 1962, 1972, and 1974 [157] 
Genetic Education Modules for Teachers — DNA from the Beginning Study Guide 
Guide to DNA cloning [159] 

Olby R (January 2003). "Quiet debut for the double helix" [160] . Nature 421 (6921): 402-5. 
doi:10.1038/nature01397. PMID 12540907. 
PDB Molecule of the Month pdb23_l [161] 
Rosalind Franklin's contributions to the study of DNA 

The Register of Francis Crick Personal Papers 1938 - 2007 at Mandeville Special Collections Library, Geisel 

Library, University of California, San Diego 

U.S. National DNA Day — watch videos and participate in real-time chat with top scientists 
"Clue to chemistry of heredity found" . The New York Times. Saturday, June 13, 1953. The first American 
newspaper coverage of the discovery of the DNA structure. 
• An Introduction to DNA and Chromosomes from HOPES: Huntington's Disease Outreach Project for 

Education at Stanford 

References 

[I] Russell, Peter (2001). [Genetics. New York: Benjamin Cummings. ISBN 0-805-34553-1. 

[2] Saenger, Wolfram (1984). Principles of Nucleic Acid Structure. New York: Springer-Verlag. ISBN 0387907629. 

[3] Alberts, Bruce; Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts and Peter Walters (2002). Molecular Biology of the Cell; 

Fourth Edition (http://www.ncbi.nlm.nih.gov/books/bv.fcgi7caltbv. View. .ShowTOC&rid=mboc4.TOC&depth=2). New York and 

London: Garland Science. ISBN 0-8153-3218-1. OCLC 145080076 48122761 57023651 69932405. . 
[4] Butler, John M. (2001). Forensic DNA Typing. Elsevier. ISBN 978-0-12-147951-0. OCLC 223032110 45406517. pp. 14-15. 
[5] Mandelkern M, Elias J, Eden D, Crothers D (1981). "The dimensions of DNA in solution". J MolBiol 152 (1): 153-61. 

doi:10.1016/0022-2836(81)90099-l. PMID 7338906. 
[6] Gregory S; Barlow, KF; McLay, KE; Kaul, R; Swarbreck, D; Dunham, A; Scott, CE; Howe, KL et al. (2006). "The DNA sequence and 

biological annotation of human chromosome 1". Nature 441 (7091): 315-21. doi:10.1038/nature04727. PMID 16710414. 
[7] Watson J.D. and Crick F.H.C. (1953). "A Structure for Deoxyribose Nucleic Acid" (http://www.nature.com/nature/dna50/watsoncrick. 

pdf) (PDF). Nature 171 (4356): 737-738. doi:10.1038/171737a0. PMID 13054692. . Retrieved 4 May 2009. 
[8] Berg J., Tymoczko J. and Stryer L. (2002) Biochemistry. W. H. Freeman and Company ISBN 0-7167-4955-6 
[9] Abbreviations and Symbols for Nucleic Acids, Polynucleotides and their Constituents (http://www.chem.qmul.ac.uk/iupac/misc/naabb. 

html) IUPAC-IUB Commission on Biochemical Nomenclature (CBN), Accessed 03 January 2006 
[10] Ghosh A, Bansal M (2003). "A glossary of DNA structures from A to Z". Acta Crystallogr D Biol Crystallogr 59 (Pt 4): 620-6. 

doi:10.1107/S0907444903003251. PMID 12657780. 

[II] Created from PDB 1D65 (http://www.rcsb. org/pdb/cgi/explore.cgi?pdbId=lD65) 



DNA 2U 

[12] Verma S, Eckstein F (1998). "Modified oligonucleotides: synthesis and strategy for users". Annu. Rev. Biochem. 67: 99—134. 

doi:10.1146/annurev.biochem.67.1.99. PMID 9759484. 
[13] Wing R, Drew H, Takano T, Broka C, Tanaka S, Itakura K, Dickerson R (1980). "Crystal structure analysis of a complete turn of B-DNA". 

Nature 287 (5784): 755-8. doi:10.1038/287755a0. PMID 7432492. 
[14] Pabo C, Sauer R (1984). "Protein-DNA recognition". Annu Rev Biochem 53: 293-321. doi:10.1 146/annurev.bi.53.070184.001453. 

PMID 6236744. 
[15] Clausen-Schaumann H, Rief M, Tolksdorf C, Gaub H (2000). "Mechanical stability of single DNA molecules" (http://www. 

pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1300792). Biophys J 78 (4): 1997—2007. 

doi:10.1016/S0006-3495(00)76747-6. PMID 10733978. PMC 1300792. 
[16] Yakovchuk P, Protozanova E, Frank-Kamenetskii MD (2006). "Base-stacking and base-pairing contributions into thermal stability of the 

DNA double helix" (http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=16449200). Nucleic Acids Res. 34 (2): 564—74. 

doi:10.1093/nar/gkj454. PMID 16449200. PMC 1360284. . 
[17] Chalikian T, Volker J, Plum G, Breslauer K (1999). "A more unified picture for the thermodynamics of nucleic acid duplex melting: a 

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artid=22151). Proc Natl Acad Sci USA 96 (14): 7853-8. doi:10.1073/pnas.96.14.7853. PMID 10393911. PMC 22151. 
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transcripts/2706israel.html) (last accessed on 4 March 2006) 
[130] Kleiman, Yaakov. "The Cohanim/DNA Connection: The fascinating story of how DNA studies confirm an ancient biblical tradition". 

(http://www.aish.com/societywork/sciencenature/the_cohanim_-_dna_connection.asp) aish.com (January 13, 2000). Accessed 4 March 

2006. 
[131] Bhattacharya, Shaoni. "Killer convicted thanks to relative's DNA". (http://www. newscientist.com/article.ns ?id=dn4908) 

newscientist.com (20 April 2004). Accessed 22 December 06 
[132] Dahm R (January 2008). "Discovering DNA: Friedrich Miescher and the early years of nucleic acid research". Hum. Genet. 122 (6): 

565-81. doi:10.1007/s00439-007-0433-0. PMID 17901982. 
[133] Levene P, (1 December 1919). "The structure of yeast nucleic acid" (http://www.jbc.Org/cgi/reprint/40/2/415). J Biol Chem 40 (2): 

415-24. . 
[134] Astbury W, (1947). "Nucleic acid". Symp. SOC. Exp. Bbl 1 (66). 
[135] Lorenz MG, Wackernagel W (1 September 1994). "Bacterial gene transfer by natural genetic transformation in the environment" (http:// 

mmbr.asm.org/cgi/pmidlookup?view=long&pmid=7968924). Microbiol. Rev. 58 (3): 563-602. PMID 7968924. PMC 372978. . 
[136] Avery O, MacLeod C, McCarty M (1944). "Studies on the chemical nature of the substance inducing transformation of pneumococcal 

types. Inductions of transformation by a desoxyribonucleic acid fraction isolated from pneumococcus type III" (http://www.jem.org/cgi/ 

reprint/149/2/297). J Exp Medl9 (2): 137-158. doi:10.1084/jem.79.2.137. PMID 19871359. PMC 2135445. . 
[137] Hershey A, Chase M (1952). "Independent functions of viral protein and nucleic acid in growth of bacteriophage" (http://www.jgp.org/ 

cgi/reprint/36/l/39.pdf) (PDF). J Gen Physiol 36 (1): 39-56. doi:10.1085/jgp.36.1.39. PMID 12981234. PMC 2147348. . 
[138] The B-DNA X-ray pattern on the right of this linked image (http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/dna/ 

pictures/sci9.001.5.html) was obtained by Rosalind Franklin and Raymond Gosling in May 1952 at high hydration levels of DNA and it has 

been labeled as "Photo 51" 
[139] Nature Archives Double Helix of DNA: 50 Years (http://www.nature.com/nature/dna50/archive.html) 
[140] Original X-ray diffraction image (http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/dna/pictures/franklin-typeBphoto. 

html) 
[141] The Nobel Prize in Physiology or Medicine 1962 (http://nobelprize.org/nobel_prizes/medicine/laureates/1962/) Nobelprize .org 

Accessed 22 December 06 
[142] Brenda Maddox (23 January 2003). "The double helix and the 'wronged heroine'" (http://www.biomath.nyu.edu/index/course/ 

hw_articles/nature4.pdf) (PDF). Nature 421 (6921): 407-408. doi:10.1038/nature01399. PMID 12540909. . 
[143] Crick, F.H.C. On degenerate templates and the adaptor hypothesis (PDF), (http://genome.wellcome.ac.uk/assets/wtx030893.pdf) 

genome.wellcome.ac.uk (Lecture, 1955). Accessed 22 December 2006 
[144] Meselson M, Stahl F (1958). "The replication of DNA in Escherichia coli" (http://www.pubmedcentral.nih.gov/articlerender. 

fcgi?tool=pmcentrez&artid=528642). P roc Natl Acad Sci USA 44 (7): 671-82. doi:10.1073/pnas.44.7.671. PMID 16590258. PMC 528642. 
[145] The Nobel Prize in Physiology or Medicine 1968 (http://nobelprize.org/nobel_prizes/medicine/laureates/1968/) Nobelprize.org 

Accessed 22 December 06 
[146] http://proteopedia.org/wiki/index.php/DNA 

[147] http://www.dmoz.Org/Science/Biology/Biochemistry_and_Molecular_Biology/Biomolecules/Nucleic_Acids/DNA// 
[148] http ://pipe. scs. fsu. edu/displar.html 
[149] http://biostudio.com/c_%20education%20mac.htm 
[150] http://www.dnaftb.org/dnaftb/ 
[151] http://ca.youtube.com/watch?v=iyb7fwduuGM 

[152] http://nobelprize.org/educational_games/medicine/dna_double_helix/ 
[153] http://www.fidelitysystems.com/Unlinked_DNA.html 
[154] http://www.dnalc.org/ 

[155] http://www.nature.com/nature/dna50/archive.html 
[156] http://www.ncbe.reading.ac.uk/DNA50/ 

[157] http://www.bbc.co.uk/bbcfour/audiointerviews/profilepages/crickwatsonl.shtml 
[158] http://www.genome.gov/10506718 

[159] http://www.blackwellpublishing.com/trun/artwork/Animations/cloningexp/cloningexp.html 
[160] http://chem-faculty.ucsd.edu/joseph/CHEM13/DNAl.pdf 

[161] http://www.rcsb.org/pdb/static.do?p=education_discussion/molecule_of_the_month/pdb23_l.html 
[162] http://mason.gmu.edu/~emoody/rfranklin.html 
[163] http://orpheus.ucsd.edU/speccoll/testing/html/mss0660a.html#abstract 



DNA 



216 



[164] http://www.genome.gov/10506367 

[165] http://www.nytimes.com/packages/pdf/science/dna-article.pdf 

[166] http://hopes.stanford.edu/basics/dna/bO.html 



Molecular models of DNA 



Molecular models of DNA structures are representations of the molecular geometry and 
topology of Deoxyribonucleic acid (DNA) molecules using one of several means, with the 
aim of simplifying and presenting the essential, physical and chemical, properties of DNA 
molecular structures either in vivo or in vitro. These representations include closely packed 
spheres (CPK models) made of plastic, metal wires for 'skeletal models', graphic 
computations and animations by computers, artistic rendering. Computer molecular models 
also allow animations and molecular dynamics simulations that are very important for 
understanding how DNA functions in vivo. 

The more advanced, computer-based molecular models of DNA involve molecular dynamics 

simulations as well as quantum mechanical computations of vibro-rotations, delocalized 

molecular orbitals (MOs), electric dipole moments, hydrogen-bonding, and so on. DNA 

molecular dynamics modeling involves simulations of DNA molecular geometry and 

topology changes with time as a result of both intra- and inter- molecular interactions of 

DNA. Whereas molecular models of Deoxyribonucleic acid (DNA) molecules such as 

closely packed spheres (CPK models) made of plastic or metal wires for 'skeletal models' are 

useful representations of static DNA structures, their usefulness is very limited for 

representing complex DNA dynamics. Computer molecular modeling allows both animations and molecular 

dynamics simulations that are very important for understanding how DNA functions in vivo. 




Spinning DNA 
generic model. 



History 



Double Helix 
Discovery 




William Astbury 
Oswald Avery 
Francis Crick 
Erwin Chargaff 
Max DelbrUck 
Jerry Donohue 
Rosalind Franklin 
Raymond Gosling 
Phoebus Levene 



Molecular models of DNA 217 

Linus Pauling 
Sir John Randall 
Erwin Schrodinger 
Alex Stokes 
James Watson 
Maurice Wilkins 
Herbert Wilson 

From the very early stages of structural studies of DNA by X-ray diffraction and biochemical means, molecular 
models such as the Watson-Crick double-helix model were successfully employed to solve the 'puzzle' of DNA 
structure, and also find how the latter relates to its key functions in living cells. The first high quality X-ray 
diffraction patterns of A-DNA were reported by Rosalind Franklin and Raymond Gosling in 1953 . The first 
calculations of the Fourier transform of an atomic helix were reported one year earlier by Cochran, Crick and Vand 
, and were followed in 1953 by the computation of the Fourier transform of a coiled-coil by Crick . 

Structural information is generated from X-ray diffraction studies of oriented DNA fibers with the help of molecular 
models of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns. 

T41 
The first reports of a double-helix molecular model of B-DNA structure were made by Watson and Crick in 1953 

. Last-but-not-least, Maurice F. Wilkins, A. Stokes and H.R. Wilson, reported the first X-ray patterns of in vivo 

B-DNA in partially oriented salmon sperm heads . The development of the first correct double-helix molecular 

model of DNA by Crick and Watson may not have been possible without the biochemical evidence for the 

nucleotide base-pairing ([A— T]; [C— G]), or Chargaffs rules .Although such initial studies of 

DNA structures with the help of molecular models were essentially static, their consequences for explaining the in 

vivo functions of DNA were significant in the areas of protein biosynthesis and the quasi-universality of the genetic 

code. Epigenetic transformation studies of DNA in vivo were however much slower to develop in spite of their 

importance for embryology, morphogenesis and cancer research. Such chemical dynamics and biochemical reactions 

of DNA are much more complex than the molecular dynamics of DNA physical interactions with water, ions and 

proteins/enzymes in living cells. 

Importance 

An old standing dynamic problem is how DNA "self -replication" takes place in living cells that should involve 
transient uncoiling of supercoiled DNA fibers. Although DNA consists of relatively rigid, very large elongated 
biopolymer molecules called "fibers" or chains (that are made of repeating nucleotide units of four basic types, 
attached to deoxyribose and phosphate groups), its molecular structure in vivo undergoes dynamic configuration 
changes that involve dynamically attached water molecules and ions. Supercoiling, packing with histones in 
chromosome structures, and other such supramolecular aspects also involve in vivo DNA topology which is even 
more complex than DNA molecular geometry, thus turning molecular modeling of DNA into an especially 
challenging problem for both molecular biologists and biotechnologists. Like other large molecules and biopolymers, 
DNA often exists in multiple stable geometries (that is, it exhibits conformational isomerism) and configurational, 
quantum states which are close to each other in energy on the potential energy surface of the DNA molecule. 



Molecular models of DNA 



218 



Such varying molecular geometries can also be computed, at least in 
principle, by employing ab initio quantum chemistry methods that can 
attain high accuracy for small molecules, although claims that 
acceptable accuracy can be also achieved for polynucleotides, as well 
as DNA conformations, were recently made on the basis of VCD 
spectral data. Such quantum geometries define an important class of ab 
initio molecular models of DNA whose exploration has barely started 
especially in connection with results obtained by VCD in solutions. 
More detailed comparisons with such ab initio quantum computations 
are in principle obtainable through 2D-FT NMR spectroscopy and 
relaxation studies of polynucleotide solutions or specifically labeled DNA, as for example with deuterium labels. 

In an interesting twist of roles, the DNA molecule itself was proposed to be utilized for quantum computing. Both 
DNA nanostructures as well as DNA 'computing' biochips have been built (see biochip image at left). 




DNA computing biochip:3D 



Examples of DNA molecular models 

Animated molecular models allow one to visually explore the three-dimensional (3D) structure of DNA. One 
visualization of DNA model is a space-filling, or CPK, model. Another is a wire, or skeletal type. 

The hydrogen bonding dynamics and proton exchange is very different by many orders of magnitude between the 
two systems of fully hydrated DNA and water molecules in ice. Thus, the DNA dynamics is complex, involving 
nanosecond and several tens of picosecond time scales, whereas that of liquid ice is on the picosecond time scale, 
and that of proton exchange in ice is on the millisecond time scale; the proton exchange rates in DNA and attached 
proteins may vary from picosecond to nanosecond, minutes or years, depending on the exact locations of the 
exchanged protons in the large biopolymers. 

A simple harmonic oscillator 'vibration' is only an oversimplified dynamic representation of the longitudinal 
vibrations of the DNA intertwined helices which were found to be anharmonic rather than harmonic as often 
assumed in quantum dynamic simulations of DNA. 




DNA Spacefilling molecular model 



Paracrystalline lattice models of B-DNA structures 

A paracrystalline lattice, or paracrystal, is a molecular or atomic lattice with significant amounts (e.g., larger than a 
few percent) of partial disordering of molecular arranegements. Limiting cases of the paracrystal model are 
nanostructures, such as glasses, liquids, etc., that may possess only local ordering and no global order. Liquid 
crystals also have paracrystalline rather than crystalline structures. 

Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which is a dynamic one in 
spite of the relatively rigid DNA double-helix stabilized by parallel hydrogen bonds between the nucleotide 
base-pairs in the two complementary, helical DNA chains (see figures). For simplicity most DNA molecular models 
ommit both water and ions dynamically bound to B-DNA, and are thus less useful for understanding the dynamic 
behaviors of B-DNA in vivo. The physical and mathematical analysis of X-ray and spectroscopic data for 

paracrystalline B-DNA is therefore much more complicated than that of crystalline, A-DNA X-ray diffraction 
patterns. The paracrystal model is also important for DNA technological applications such as DNA nanotechnology. 



Molecular models of DNA 219 

Novel techniques that combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now 
;o 

] ). 



also being developed (see, for example, "Application of X-ray microscopy in the analysis of living hydrated cells" 

[15], 



Genomic and biotechnology applications of DNA molecular modeling 

There are various uses of DNA molecular modeling in Genomics and Biotechnology research applications, from 
DNA repair to PCR and DNA nanostructures. Two-dimensional DNA junction arrays have been visualized by 
Atomic force microscopy. 

Quadruplex DNA may be involved in certain cancers 

See also 

DNA structure 

X-ray scattering 

Neutron scattering 

Crystallography 

Crystal lattices 

2D-FT NMRI and Spectroscopy 

List of nucleic acid simulation software 

Sirius visualization software 

X-ray microscopy 

QMC@Home 

Sir Lawrence Bragg, FRS 

Spectroscopy 

• Vibrational circular dichroism (VCD) 

• FT-NMR [20] [21] 

• NMR Atlas-database [22] 

T231 

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data 

• NMR constraints files for NAs in PDB format 

[25] 

NMR microscopy 
Microwave spectroscopy 
FT-IR 

FT-NIR [26] [27] [28] 

Spectral, Hyperspectral, and Chemical imaging) 

Raman spectroscopy/microscopy and CARS 

Fluorescence correlation spectroscopy , Fluorescence cross-correlation 

a ddetI 42 ! [43] [44] 

spectroscopy and FRET 
Confocal microscopy 



Molecular models of DNA 220 

Further reading 

• Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology .(June 2004) I. C. 
Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin., q-bio/0406047. 

• F. Bessel, Untersuchung des Theils der planetarischen Storungen, Berlin Abhandlungen (1824), article 14. 

• Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and Sons, Ltd., vols. 1 and 
2., 1966., 2024 pages. 

• Cantor, C. R. and Schimmel, P.R. Biophysical Chemistry, Parts I and II., San Franscisco: W.H. Freeman and Co. 
1980. 1,800 pages. 

• Voet, D. and J.G. Voet. Biochemistry, 2nd Edn., New York, Toronto, Singapore: John Wiley & Sons, Inc., 1995, 
ISBN0-471-58651-X., 1361 pages. 

• Watson, G. N. A Treatise on the Theory of Bessel Functions., (1995) Cambridge University Press. ISBN 
0-521-48391-3. 

• Watson, James D. Molecular Biology of the Gene. New York and Amsterdam: W.A. Benjamin, Inc. 1965., 494 
pages. 

• Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science, Inc. 2000. 

• Herbert R. Wilson, FRS. Diffraction of X-rays by proteins, Nucleic Acids and Viruses., London: Edward Arnold 
(Publishers) Ltd. 1966. 

• Kurt Wuthrich. NMR of Proteins and Nucleic Acids., New York, Brisbane,Chicester, Toronto, Singapore: J. 
Wiley & Sons. 1986., 292 pages. 

• Robinson, Bruche H.; Seeman, Nadrian C. (August 1987). "The Design of a Biochip: A Self-Assembling 
Molecular-Scale Memory Device". Protein Engineering 1 (4): 295-300. ISSN 0269-2139. Link [45] 

• Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson, Deborah Kuchnir & 
Winfree, Erik (22 December 2004). "Design and Characterization of Programmable DNA Nanotubes". Journal of 
the American Chemical Society 126 (50): 16344-16352. doi:10.1021/ja0443191. ISSN 0002-7863. 

• Keren, K; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun (November 2003). 
"DNA-Templated Carbon Nanotube Field-Effect Transistor" [46] . Science 302 (6549): 1380-1382. 

doi: 10. 1126/science. 1091022. ISSN 1095-9203. 

• Zheng, Jiwen; Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl, Richard A. & Seeman 
Nadrian C. (2006). "2D Nanoparticle Arrays Show the Organizational Power of Robust DNA Motifs". Nano 
Letters 6: 1502-1504. doi:10.1021/nl060994c. ISSN 1530-6984. 

• Cohen, Justin D.; Sadowski, John P.; Dervan, Peter B. (2007). "Addressing Single Molecules on DNA 
Nanostructures". Angewandte Chemie 46 (42): 7956-7959. doi:10.1002/anie.200702767. ISSN 0570-0833. 

• Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping; Ding, Baoquan; 
Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie & Seeman, Nadrian C. (2006). "Double 
cohesion in structural DNA nanotechnology". Organic and Biomolecular Chemistry 4: 3414—3419. 
doi:10.1039/b605212f. 

• Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic results 
and DNA sequence data". Bioinformatics 20: 3682—3686. 

• Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences". 
Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041 



Molecular models of DNA 22 1 

External links 

• DNA the Double Helix Game From the official Nobel Prize web site 

• MDDNA: Structural Bioinformatics of DNA [47] 

• Double Helix 1953—2003 National Centre for Biotechnology Education 

• DNAlive: a web interface to compute DNA physical properties . Also allows cross-linking of the results with 

the UCSC Genome browser and DNA dynamics. 

[491 

• DiProDB: Dinucleotide Property Database . The database is designed to collect and analyse thermodynamic, 

structural and other dinucleotide properties. 

• Further details of mathematical and molecular analysis of DNA structure based on X-ray data 

• Bessel functions corresponding to Fourier transforms of atomic or molecular helices. 

• Application of X-ray microscopy in analysis of living hydrated cells 

T521 

• overview of STM/AFM/SNOM principles with educative videos 

Databases for DNA molecular models and sequences 
X-ray diffraction 

• NDB ID: UD0017 Database [17] 

• X-ray Atlas -database 

T541 

• PDB files of coordinates for nucleic acid structures from X-ray diffraction by NA (incl. DNA) crystals 

• Structure factors dowloadable files in CIF format 
Neutron scattering 



• ISIS neutron source: ISIS pulsed neutron source:A world centre for science with neutrons & muons at Harwell, 
near Oxford, UK. 

X-ray microscopy 

• Application of X 
Electron microscopy 

• DNA under electron microscope 



Application of X-ray microscopy in the analysis of living hydrated cells 



Genomic and structural databases 

— contains examples of base skews. 

[58] 



T571 
• CBS Genome Atlas Database — contains examples of base skews. 



• The Z curve database of genomes — a 3-dimensional visualization and analysis tool of genomes 

• DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids molecular structure models in 
PDB and CIF formats [59] 

Atomic force microscopy 

• How SPM Works [60] 

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [61] 



Molecular models of DNA 222 

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[2] Cochran, W., Crick, F.H.C. and Vand V. 1952. The Structure of Synthetic Polypeptides. 1. The Transform of Atoms on a Helix. Acta Cryst. 

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[20] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants 
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Javascript-like NMR coupling constant to dihedral 
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91,5740-5747. 



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[37] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in biotechnology, (1995) J. 

Biotechnol., 41,177-186. 
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determination in protein— DNA complexes. Current Opinion in Structural Biology 2001, 11(2), 201-207 



[44] http 

[45] http 

[46] http 

[47] http 

[48] http 

[49] http 

[50] http 

[51] http 

[52] http 

[53] http 

[54] http 

[55] http 

[56] http 

[57] http 

[58] http 

[59] http 

[60] http 

[61] http 



//www. fretimaging.org/mcnamaraintro. html FRET imaging introduction 

//peds.oxfordjournals.org/cgi/content/abstract/1/4/295 

//www.sciencemag.org/cgi/content/abstract/sci;302/5649/1380 

//humphry.chem.wesleyan.edu:8080/MDDNA/ 

//mmb. pcb.ub.es/DNAlive 

//diprodb.fli-leibniz.de 

//planetphysics. org/ encyclopedia/BesselFunctionsApplicationsToDiffrac tionByHelicalStructures.html 

//planetphysics.org/?op=getobj&from=objects&name=BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures 

//www. ntmdt.ru/SPM-Techniques/Principles/ 

//ndbserver.rutgers.edu/atlas/xray/index.html 

//ndbserver.rutgers.edu/ftp/NDB/coordinates/na-biol/ 

//ndbserver.rutgers.edu/ftp/NDB/structure-factors/ 

//www. isis.rl.ac.uk/ 

//www. cbs.dtu.dk/services/GenomeAtlas/ 

//tubic. tju.edu.cn/zcurve/ 

//ndbserver.rutgers.edu/ftp/NDB/models/ 

//www. parkafm.com/New_html/resources/01general.php 

//www. rhk-tech.com/results/showcase.php 



DNA structure 224 



DNA structure 



The structure of DNA shows a variety of forms, both double-stranded and single-stranded. The mechanical 
properties of DNA, which are directly related to its structure, are a significant problem for cells. Every process which 
binds or reads DNA is able to use or modify the mechanical properties of DNA for purposes of recognition, 
packaging and modification. The extreme length (a chromosome may contain a 10 cm long DNA strand), relative 
rigidity and helical structure of DNA has led to the evolution of histones and of enzymes such as topoisomerases and 
helicases to manage a cell's DNA. The properties of DNA are closely related to its molecular structure and sequence, 
particularly the weakness of the hydrogen bonds and electronic interactions that hold strands of DNA together 
compared to the strength of the bonds within each strand. 

Experimental techniques which can directly measure the mechanical properties of DNA are relatively new, and 
high-resolution visualization in solution is often difficult. Nevertheless, scientists have uncovered large amount of 
data on the mechanical properties of this polymer, and the implications of DNA's mechanical properties on cellular 
processes is a topic of active current research. 

The DNA found in many cells can be macroscopic in length - a few centimetres long for each human chromosome. 
Consequently, cells must compact or "package" DNA to carry it within them. In eukaryotes this is carried by 
spool-like proteins known as histones, around which DNA winds. It is the further compaction of this DNA-protein 
complex which produces the well known mitotic eukaryotic chromosomes. 

Structure determination 

DNA structures can be determined using either nuclear magnetic resonance spectroscopy or X-ray crystallography. 
The first published reports of A-DNA X-ray diffraction patterns— and also B-DNA — employed analyses based on 
Patterson transforms that provided only a limited amount of structural information for oriented fibers of DNA 
isolated from calf thymus. An alternate analysis was then proposed by Wilkins et al. in 1953 for B-DNA X-ray 

diffraction/scattering patterns of hydrated, bacterial oriented DNA fibers and trout sperm heads in terms of squares 
of Bessel functions. Although the "B-DNA form' is most common under the conditions found in cells, it is not a 
well-defined conformation but a family or fuzzy set of DNA-conformations that occur at the high hydration levels 
present in a wide variety of living cells. Their corresponding X-ray diffraction & scattering patterns are 
characteristic of molecular paracrystals with a significant degree of disorder (>20%) , and concomitantly the 

structure is not tractable using only the standard analysis. 

ro] 

On the other hand, the standard analysis, involving only Fourier transforms of Bessel functions and DNA 
molecular models, is still routinely employed for the analysis of A-DNA and Z-DNA X-ray diffraction patterns. 

Base pair geometry 

The geometry of a base, or base pair step can be characterized by 6 coordinates: Shift, Slide, Rise, Tilt, Roll, and 
Twist. These values precisely define the location and orientation in space of every base or base pair in a DNA 
molecule relative to its predecessor along the axis of the helix. Together, they characterize the helical structure of the 
molecule. In regions of DNA where the "normal" structure is disrupted the change in these values can be used to 
describe such disruption. 

For each base pair, considered relative to its predecessor : 

• Shear 

• Stretch 

• Stagger 

• Buckle 



DNA structure 225 

Propeller twist: Rotation of one base with respect to the other in the same base pair. 

Opening 

Shift: displacement along an axis in the base-pair plane perpendicular to the first, directed from the minor to the 
major groove. 

Slide: displacement along an axis in the plane of the base pair directed from one strand to the other. 

Rise: displacement along the helix axis. 

Tilt: rotation around this axis. 

Roll: rotation around this axis. 

Twist: rotation around the helix axis. 

x-displacement 

y-displacement 

inclination 

tip 

pitch: the number of base pairs per complete turn of the helix 

Rise and twist determine the handedness and pitch of the helix. The other coordinates, by contrast, can be zero. Slide 
and shift are typically small in B-DNA, but are substantial in A- and Z-DNA. Roll and tilt make successive base 
pairs less parallel, and are typically small. A diagram of these coordinates can be found in 3DNA website. 

Note that "tilt" has often been used differently in the scientific literature, referring to the deviation of the first, 
inter-strand base-pair axis from perpendicularity to the helix axis. This corresponds to slide between a succession of 
base pairs, and in helix-based coordinates is properly termed "inclination". 



DNA helix geometries 



Three DNA conformations are believed to be found in nature, A-DNA, B-DNA, and Z-DNA. The "B" form 
described by James D. Watson and Francis Crick is believed to predominate in cells . It is 23.7 A wide and 
extends 34 A per 10 bp of sequence. The double helix makes one complete turn about its axis every 10.4-10.5 base 
pairs in solution. This frequency of twist (known as the helical pitch) depends largely on stacking forces that each 
base exerts on its neighbours in the chain. 

Other conformations are possible; A-DNA, B-DNA, C-DNA, D-DNA [16] , E-DNA [17] , L-DNA(enantiomeric form 
of D-DNA) [16] , P-DNA [18] , S-DNA, Z-DNA, etc. have been described so far. [19] In fact, only the letters F, Q, U, V, 
and Y are now available to describe any new DNA structure that may appear in the future. However, most of 

these forms have been created synthetically and have not been observed in naturally occurring biological systems. 
Also note the triple-stranded DNA possibility. 

A- and Z-DNA 

A-DNA and Z-DNA differ significantly in their geometry and dimensions to B-DNA, although still form helical 
structures. The A form appears likely to occur only in dehydrated samples of DNA, such as those used in 
crystallographic experiments, and possibly in hybrid pairings of DNA and RNA strands. Segments of DNA that cells 
have methylated for regulatory purposes may adopt the Z geometry, in which the strands turn about the helical axis 
the opposite way to A-DNA and B-DNA. There is also evidence of protein-DNA complexes forming Z-DNA 
structures. 



DNA structure 



226 





The structures of A-, B-, and Z-DNA. 



Guanine 



o 



..-H— N 



Cytosine 



^ o b r*> anti 




C5' 



axis of helix 
of Z-DNA 



The helix axis of A-, B-, and Z-DNA. 



Structural features of the three major forms of DNA 



Geometry attribute 


A-DNA 


B-DNA 


Z-DNA 


Helix sense 


right-handed 


right-handed 


left-handed 


Repeating unit 


lbp 


lbp 


2bp 


Rotation/bp 


33.6° 


35.9° 


6072bp 


Mean bp/turn 


10.7 


10.0 


12 


Inclination of bp to 
axis 


+19° 


-1.2° 


-9° 


Rise/bp along axis 


2.3 A 


3.32 A 


3.8 A 


Pitch/turn of helix 


24.6 A 


33.2 A 


45.6 A 


Mean propeller twist 


+18° 


+16° 


0° 


Glycosyl angle 


anti 


anti 


C: anti, 
G: syn 


Sugar pucker 


C3'-endo 


C2'-endo 


C: 

C2'-endo, 
G: C2'-exo 


Diameter 


25.5 A 


23.7 A 


18.4 A 



Supercoiled DNA 

The B form of the DNA helix twists 360° per 10.4-10.5 bp in the absence of torsional strain. But many molecular 
biological processes can induce torsional strain. A DNA segment with excess or insufficient helical twisting is 
referred to, respectively, as positively or negatively "supercoiled". DNA in vivo is typically negatively supercoiled, 
which facilitates the unwinding (melting) of the double-helix required for RNA transcription. 



Non-helical forms 

Other non-double helical forms of DNA have been described, for example side-by-side (SBS) and triple helical 
configurations. Single stranded DNA may exist in statu nascendi or as thermally induced despiralized DNA. 



DNA structure 



227 



DNA bending 

DNA is a relatively rigid polymer, typically modelled as a worm-like chain. It has three significant degrees of 
freedom; bending, twisting and compression, each of which cause particular limitations on what is possible with 
DNA within a cell. Twisting/torsional stiffness is important for the circularisation of DNA and the orientation of 
DNA bound proteins relative to each other and bending/axial stiffness is important for DNA wrapping and 
circularisation and protein interactions. Compression/extension is relatively unimportant in the absence of high 
tension. 

Persistence length/Axial stiffness 

Example sequences and their persistence lengths (B DNA) 



Sequence 


Persistence 

Length 
/base pairs 


Random 


154+10 


(CA) 

repeat 


133±10 


(CAG) 

repeat 


124±10 


(TATA) 

repeat 


137±10 



DNA in solution does not take a rigid structure but is continually changing conformation due to thermal vibration 
and collisions with water molecules, which makes classical measures of rigidity impossible. Hence, the bending 
stiffness of DNA is measured by the persistence length, defined as: 

"The length of DNA over which the time-averaged orientation of the polymer becomes uncorrelated by a 
factor of e." 

This value may be directly measured using an atomic force microscope to directly image DNA molecules of various 
lengths. In aqueous solution the average persistence length is 46-50 nm or 140-150 base pairs (the diameter of DNA 
is 2 nm), although can vary significantly. This makes DNA a moderately stiff molecule. 

The persistence length of a section of DNA is somewhat dependent on its sequence, and this can cause significant 
variation. The variation is largely due to base stacking energies and the residues which extend into the minor and 
major grooves. 

Models for DNA bending 



Stacking stability of base steps (B DNA) 



Step 


Stacking 

AG 
/kcal mol" 


TA 


-0.19 


T G or C A 


-0.55 


CG 


-0.91 


A G or C T 


-1.06 


A A or T T 


-1.11 


AT 


-1.34 



DNA structure 228 



G A or T C 


-1.43 


CCorG 
G 


-1.44 


A C or G T 


-1.81 


GC 


-2.17 



The entropic flexibility of DNA is remarkably consistent with standard polymer physics models such as the 
Kratky-Porod worm-like chain model. Consistent with the worm-like chain model is the observation that bending 
DNA is also described by Hooke's law at very small (sub-piconewton) forces. However for DNA segments less than 
the persistence length, the bending force is approximately constant and behaviour deviates from the worm-like chain 
predictions. 

This effect results in unusual ease in circularising small DNA molecules and a higher probability of finding highly 
bent sections of DNA. 

Bending preference 

DNA molecules often have a preferred direction to bend, ie. anisotropic bending. This is, again, due to the properties 
of the bases which make up the DNA sequence - a random sequence will have no preferred bend direction, i.e. 
isotropic bending. 

Preferred DNA bend direction is determined by the stability of stacking each base on top of the next. If unstable base 
stacking steps are always found on one side of the DNA helix then the DNA will preferentially bend away from that 
direction. As bend angle increases then steric hindrances and ability to roll the residues relative to each other also 
play a role, especially in the minor groove. A and T residues will be preferentially be found in the minor grooves on 
the inside of bends. This effect is particularly seen in DNA-protein binding where tight DNA bending is induced, 
such as in nucleosome particles. See base step distortions above. 

DNA molecules with exceptional bending preference can become intrinsically bent. This was first observed in 
trypanosomatid kinetoplast DNA. Typical sequences which cause this contain stretches of 4-6 T and A residues 
separated by G and C rich sections which keep the A and T residues in phase with the minor groove on one side of 
the molecule. For example: 



I I I I 

I I 

GATTCCCAAAAATGTCAAAAAATAGGCAAAAAATGC 
CAAAAAATCCCAAAC 

The intrinsically bent structure is induced by the 'propeller twist' of base pairs relative to each other allowing unusual 
bifurcated Hydrogen-bonds between base steps. At higher temperatures this structure, and so the intrinsic bend, is 
lost. 

All DNA which bends anisotropically has, on average, a longer persistence length and greater axial stiffness. This 
increased rigidity is required to prevent random bending which would make the molecule act isotropically. 

DNA circularization 

DNA circularization depends on both the axial (bending) stiffness and torsional (rotational) stiffness of the molecule. 
For a DNA molecule to successfully circularize it must be long enough to easily bend into the full circle and must 
have the correct number of bases so the ends are in the correct rotation to allow bonding to occur. The optimum 
length for circularization of DNA is around 400 base pairs (136 nm), with an integral number of turns of the DNA 
helix, i.e. multiples of 10.4 base pairs. Having a non integral number of turns presents a significant energy barrier for 
circularization, for example a 10.4 x 30 = 312 base pair molecule will circularize hundreds of times faster than 10.4 x 



DNA structure 



229 



30.5 ~ 317 base pair molecule. 



DNA stretching 

Longer stretches of DNA are entropically elastic under tension. When DNA is in solution, it undergoes continuous 
structural variations due to the energy available in the solvent. This is due to the thermal vibration of the molecule 
combined with continual collisions with water molecules. For entropic reasons, more compact relaxed states are 
thermally accessible than stretched out states, and so DNA molecules are almost universally found in a tangled 
relaxed layouts. For this reason, a single molecule of DNA will stretch under a force, straightening it out. Using 
optical tweezers, the entropic stretching behavior of DNA has been studied and analyzed from a polymer physics 
perspective, and it has been found that DNA behaves largely like the Kratky-Porod worm-like chain model under 
physiologically accessible energy scales. 

Under sufficient tension and positive torque, DNA is thought to undergo a phase transition with the bases splaying 

outwards and the phosphates moving to the middle. This proposed structure for overstretched DNA has been called 

n si 
"P-form DNA," in honor of Linus Pauling who originally presented it as a possible structure of DNA 

The mechanical properties DNA under compression have not been characterized due to experimental difficulties in 
preventing the polymer from bending under the compressive force. 



DNA melting 



Melting stability of base steps (B DNA) 



Step 


Melting 

AG 

/Kcal mol" 1 


TA 


-0.12 


T G or C A 


-0.78 


CG 


-1.44 


A G or C T 


-1.29 


A A or T T 


-1.04 


AT 


-1.27 


G A or T C 


-1.66 


CCorG 
G 


-1.97 


A C or G T 


-2.04 


GC 


-2.70 



DNA melting is the process by which the interactions between the strands of the double helix are broken, separating 

the two strands of DNA. These bonds are weak, easily separated by gentle heating, enzymes, or physical force. DNA 

T221 
melting preferentially occurs at certain points in the DNA. T and A rich sequences are more easily melted than C 

and G rich regions. Particular base steps are also susceptible to DNA melting, particularly T A and T G base 

steps. These mechanical features are reflected by the use of sequences such as TATAA at the start of many genes 

to assist RNA polymerase in melting the DNA for transcription. 

Strand separation by gentle heating, as used in PCR, is simple providing the molecules have fewer than about 10,000 
base pairs (10 kilobase pairs, or 10 kbp). The intertwining of the DNA strands makes long segments difficult to 
separate. The cell avoids this problem by allowing its DNA-melting enzymes (helicases) to work concurrently with 



DNA structure 



230 



topoisomerases, which can chemically cleave the phosphate backbone of one of the strands so that it can swivel 
around the other. Helicases unwind the strands to facilitate the advance of sequence-reading enzymes such as DNA 
polymerase. 



DNA topology 

Within the cell most DNA is topologically restricted. DNA is typically 
found in closed loops (such as plasmids in prokaryotes) which are 
topologically closed, or as very long molecules whose diffusion 
coefficients produce effectively topologically closed domains. Linear 
sections of DNA are also commonly bound to proteins or physical 
structures (such as membranes) to form closed topological loops. 

Francis Crick was one of the first to propose the importance of linking 
numbers when considering DNA supercoils. In a paper published in 
1976, Crick outlined the problem as follows: 

In considering supercoils formed by closed 
double-stranded molecules of DNA certain mathematical 
concepts, such as the linking number and the twist, are 
needed. The meaning of these for a closed ribbon is 
explained and also that of the writhing number of a closed 

curve. Some simple examples are given, some of which 

T241 
may be relevant to the structure of chromatin. 

Analysis of DNA topology uses three values: 

L = linking number - the number of times one DNA strand wraps 



1 Twist = -1, Writhe = 0. 



Twist = 0, Writhe = -1. 



J Twist ^ +1 Writhe = 0. 



Twist = 0, Writhe = +1 . 



\ Twist = -2. Writhe = 0. 



Twist - 0, Writhe = 



i A 



1 



o 



\\ Twist = +2, Writhe = 0. 



Twist = 0, Writhe = +2. 



Twist = 0, Writhe = -4. 



Plectonemic 



Supercoiled structure of circular DNA molecules 

with low writhe. Note that the helical nature of 

the DNA duplex is omitted for clarity. 



around the other. It is an integer for a closed loop and constant 
for a closed topological domain. 

T = twist - total number of turns in the double stranded DNA helix. This will normally try to be equal to the 
number turns a DNA molecule will make while free in solution, ie. number of bases/10.4. 

W = writhe - number of turns of the double stranded DNA helix around the superhelical axis 

L = T + W and AL = AT + AW 

Any change of T in a closed topological domain must be balanced by a change in W, and vice versa. This results in 
higher order structure of DNA. A circular DNA molecule with a writhe of will be circular. If the twist of this 
molecule is subsequently increased or decreased by supercoiling then the writhe will be appropriately altered, 
making the molecule undergo plectonemic or toroidal superhelical coiling. 

When the ends of a piece of double stranded helical DNA are joined so that it forms a circle the strands are 
topologically knotted. This means the single strands cannot be separated any process that does not involve breaking a 
strand (such as heating). The task of un-knotting topologically linked strands of DNA falls to enzymes known as 
topoisomerases. These enzymes are dedicated to un-knotting circular DNA by cleaving one or both strands so that 
another double or single stranded segment can pass through. This un-knotting is required for the replication of 
circular DNA and various types of recombination in linear DNA which have similar topological constraints. 



DNA structure 23 1 

The linking number paradox 

For many years, the origin of residual supercoiling in eukaryotic genomes remained unclear. This topological puzzle 

T251 
was referred to by some as the "linking number paradox". However, when experimentally determined structures 

of the nucleosome displayed an overtwisted left-handed wrap of DNA around the histone octamer , this 

"paradox" was solved. 

See also 

• DNA nanotechnology 

• Molecular models of DNA 



External links 

• MDDNA: Structm 

r?8i 

• Abalone — Commercial software for DNA modeling 

• DNAlive: a web interface to compute DNA phys 
the UCSC Genome browser and DNA dynamics 

• DiProDB: Dinucleotide Property Database 
structural and other dinucleotide properties. 



MDDNA: Structural Bioinformatics of DNA [47] 

A modeling 

DNAlive: a web interface to compute DNA physical properties . Also allows cross-linking of the results with 

imic 
[491 
DiProDB: Dinucleotide Property Database . The database is designed to collect and analyse thermodynamic, 



References 

[I] Franklin, R.E. and Gosling, R.G. received 6 March 1953. Acta Cryst. (1953). 6, 673: The Structure of Sodium Thymonucleate Fibres I. The 
Influence of Water Content.; also Acta Cryst. 6, 678: The Structure of Sodium Thymonucleate Fibres II. The Cylindrically Symmetrical 
Patterson Function. 

[2] Franklin, Rosalind (1953). "Molecular Configuration in Sodium Thymonucleate. Franklin R. and Gosling R.G" (http://www.nature.com/ 

nature/dna50/franklingosling.pdf) (PDF). Nature 111. 740-741. doi:10.1038/171740a0. PMID 13054694. . 
[3] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953). "Molecular Structure of Deoxypentose Nucleic Acids" (http://www.nature.com/ 

nature/dna50/wilkins.pdf) (PDF). Nature 171: 738-740. doi:10.1038/171738a0. PMID 13054693. . 
[4] Leslie AG, Arnott S, Chandrasekaran R, Ratliff RL (1980). "Polymorphism of DNA double helices". ]. Mol. Biol. 143 (1): 49-72. 

doi: 10.1016/0022-2836(80)90124-2. PMID 7441761. 
[5] Baianu, I.C. (1980). "Structural Order and Partial Disorder in Biological systems". Bull. Math. Biol. 42 (4): 464^468. 

doi: 10.1016/0022-2836(80)90124-2. 
[6] Hosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Pubis., Amsterdam — New York, 1962 
[7] Baianu I.C, X-ray scattering by partially disordered membrane systems, Acta Cryst. A, 34 (1978), 751—753. 
[8] Bessel functions and diffraction by helical structures (http://planetphysics.org/encyclopedia/ 

BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures.html) 
[9] X-Ray Diffraction Patterns of Double-Helical Deoxyribonucleic Acid (DNA) Crystals (http://planetphysics.org/encyclopedia/ 

BesselFunctionsApplicationsToDiffractionByHelicalStructures.html) 
[10] Dickerson RE (1989). "Definitions and nomenclature of nucleic acid structure components". Nucleic Acids Res 17 (5): 1797—1803. 

doi:10.1093/nar/17.5.1797. PMID 2928107. 

[II] Lu XJ, Olson WK (1999). "Resolving the discrepancies among nucleic acid conformational analyses". J Mol Biol 285 (4): 1563—1575. 
doi:10.1006/jmbi.l998.2390. PMID 9917397. 

[12] Olson WK, Bansal M, Burley SK, Dickerson RE, Gerstein M, Harvey SC, Heinemann U, Lu XJ, Neidle S, Shakked Z, Sklenar H, Suzuki 

M, Tung CS, Westhof E, Wolberger C, Berman HM (2001). "A standard reference frame for the description of nucleic acid base-pair 

geometry". JMolBiolili (1): 229-237. doi:10.1006/jmbi.2001.4987. PMID 11601858. 
[13] http://rutchem.rutgers.edu/~xiangjun/3DNA/images/bp_step_hel.gif 
[14] http://rutchem.rutgers.edu/~xiangjun/3DNA/examples.html 

[15] Richmond, et al. (2003). "The structure of DNA in the nucleosome core". Nature 423: 145-150. doi: 10.1038/nature01595. PMID 12736678. 
[16] Hayashi G, HagiharaM, Nakatani K (2005). "Application of L-DNA as a molecular tag". Nucleic Acids Symp Ser (Oxf) 49: 261-262. 

PMID 17150733. 
[17] Vargason JM, Eichman BF, Ho PS (2000). "The extended and eccentric E-DNA structure induced by cytosine methylation or bromination". 

Nature Structural Biology 7: 758-761. doi:10.1038/78985. 
[18] Allemand, et al. (1998). "Stretched and overwound DNA forms a Pauling-like structure with exposed bases". PNAS 24: 14152—14157. 

doi:10.1073/pnas.95.24.14152. PMID 9826669. 



DNA structure 



232 



[19] List of 55 fiber structures (http://rutchem.rutgers.edu/~xiangjun/3DNA/misc/fiber_model.txt) 

[20] BansalM (2003). "DNA structure: Revisiting the Watson-Crick double helix". Current Science 85 (11): 1556-1563. 

[21] Ghosh A, Bansal M (2003). "A glossary of DNA structures from A to Z". Acta Cn'st D59: 620-626. doi:10.1107/S0907444903003251. 

[22] Breslauer KJ, Frank R, Blocker H, Marky LA (1986). "Predicting DNA duplex stability from the base sequence". PNAS 83 (11): 

3746-3750. PMID 3459152. 
[23] Richard Owczarzy (2008-08-28). "DNA melting temperature - How to calculate it?" (http://www.owczarzy.net/tm.htm). 

High-throughput DNA biophysics, owczarzy.net. . Retrieved 2008-10-02. 
[24] Crick FH (1976). "Linking numbers and nucleosomes". Proc Natl Acad Sci USA 73 (8): 2639-43. doi: 10.1073/pnas.73.8.2639. 

PMID 1066673. 
[25] Prunell A (1998). "A topological approach to nucleosome structure and dynamics: the linking number paradox and other issues". Biophys J 

74 (5): 2531-2544. PMID 9591679. 
[26] Luger K, Mader AW, Richmond RK, Sargent DF, Richmond TJ (1997). "Crystal structure of the nucleosome core particle at 2.8 A 

resolution". Nature 389 (6648): 251-260. doi:10.1038/38444. PMID 9305837. 
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[28] http://www.biomolecular-modeling.com/Abalone/index.html 



DNA Dynamics 



Molecular models of DNA structures are representations of the molecular geometry and 
topology of Deoxyribonucleic acid (DNA) molecules using one of several means, with the 
aim of simplifying and presenting the essential, physical and chemical, properties of DNA 
molecular structures either in vivo or in vitro. These representations include closely packed 
spheres (CPK models) made of plastic, metal wires for 'skeletal models', graphic 
computations and animations by computers, artistic rendering. Computer molecular models 
also allow animations and molecular dynamics simulations that are very important for 
understanding how DNA functions in vivo. 

The more advanced, computer-based molecular models of DNA involve molecular dynamics 

simulations as well as quantum mechanical computations of vibro-rotations, delocalized 

molecular orbitals (MOs), electric dipole moments, hydrogen-bonding, and so on. DNA 

molecular dynamics modeling involves simulations of DNA molecular geometry and 

topology changes with time as a result of both intra- and inter- molecular interactions of 

DNA. Whereas molecular models of Deoxyribonucleic acid (DNA) molecules such as 

closely packed spheres (CPK models) made of plastic or metal wires for 'skeletal models' are 

useful representations of static DNA structures, their usefulness is very limited for 

representing complex DNA dynamics. Computer molecular modeling allows both animations and molecular 

dynamics simulations that are very important for understanding how DNA functions in vivo. 




Spinning DNA 
generic model. 



History 



DNA Dynamics 233 



Double Helix 
Discovery 



William Astbury 
Oswald Avery 
Francis Crick 
Erwin Chargaff 
Max Delbriick 
Jerry Donohue 
Rosalind Franklin 
Raymond Gosling 
Phoebus Levene 
Linus Pauling 
Sir John Randall 
Erwin Schrodinger 
Alex Stokes 
James Watson 
Maurice Wilkins 
Herbert Wilson 

From the very early stages of structural studies of DNA by X-ray diffraction and biochemical means, molecular 
models such as the Watson-Crick double-helix model were successfully employed to solve the 'puzzle' of DNA 
structure, and also find how the latter relates to its key functions in living cells. The first high quality X-ray 
diffraction patterns of A-DNA were reported by Rosalind Franklin and Raymond Gosling in 1953 . The first 

calculations of the Fourier transform of an atomic helix were reported one year earlier by Cochran, Crick and Vand 

121 T31 

, and were followed in 1953 by the computation of the Fourier transform of a coiled-coil by Crick . 

Structural information is generated from X-ray diffraction studies of oriented DNA fibers with the help of molecular 
models of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns. 

141 
The first reports of a double-helix molecular model of B-DNA structure were made by Watson and Crick in 1953 

. Last-but-not-least, Maurice F. Wilkins, A. Stokes and H.R. Wilson, reported the first X-ray patterns of in vivo 

B-DNA in partially oriented salmon sperm heads . The development of the first correct double-helix molecular 

model of DNA by Crick and Watson may not have been possible without the biochemical evidence for the 

nucleotide base-pairing ([A— T]; [C — G]), or Chargaffs rules .Although such initial studies of 

DNA structures with the help of molecular models were essentially static, their consequences for explaining the in 

vivo functions of DNA were significant in the areas of protein biosynthesis and the quasi-universality of the genetic 

code. Epigenetic transformation studies of DNA in vivo were however much slower to develop in spite of their 

importance for embryology, morphogenesis and cancer research. Such chemical dynamics and biochemical reactions 

of DNA are much more complex than the molecular dynamics of DNA physical interactions with water, ions and 

proteins/enzymes in living cells. 



DNA Dynamics 



234 



Importance 

An old standing dynamic problem is how DNA "self -replication" takes place in living cells that should involve 
transient uncoiling of supercoiled DNA fibers. Although DNA consists of relatively rigid, very large elongated 
biopolymer molecules called "fibers" or chains (that are made of repeating nucleotide units of four basic types, 
attached to deoxyribose and phosphate groups), its molecular structure in vivo undergoes dynamic configuration 
changes that involve dynamically attached water molecules and ions. Supercoiling, packing with histones in 
chromosome structures, and other such supramolecular aspects also involve in vivo DNA topology which is even 
more complex than DNA molecular geometry, thus turning molecular modeling of DNA into an especially 
challenging problem for both molecular biologists and biotechnologists. Like other large molecules and biopolymers, 
DNA often exists in multiple stable geometries (that is, it exhibits conformational isomerism) and configurational, 
quantum states which are close to each other in energy on the potential energy surface of the DNA molecule. 

Such varying molecular geometries can also be computed, at least in 
principle, by employing ab initio quantum chemistry methods that can 
attain high accuracy for small molecules, although claims that 
acceptable accuracy can be also achieved for polynucleotides, as well 
as DNA conformations, were recently made on the basis of VCD 
spectral data. Such quantum geometries define an important class of ab 
initio molecular models of DNA whose exploration has barely started 
especially in connection with results obtained by VCD in solutions. 
More detailed comparisons with such ab initio quantum computations 
are in principle obtainable through 2D-FT NMR spectroscopy and 
relaxation studies of polynucleotide solutions or specifically labeled DNA, as for example with deuterium labels. 

In an interesting twist of roles, the DNA molecule itself was proposed to be utilized for quantum computing. Both 
DNA nanostructures as well as DNA 'computing' biochips have been built (see biochip image at left). 




Examples of DNA molecular models 

Animated molecular models allow one to visually explore the three-dimensional (3D) structure of DNA. One 
visualization of DNA model is a space-filling, or CPK, model. Another is a wire, or skeletal type. 

The hydrogen bonding dynamics and proton exchange is very different by many orders of magnitude between the 
two systems of fully hydrated DNA and water molecules in ice. Thus, the DNA dynamics is complex, involving 
nanosecond and several tens of picosecond time scales, whereas that of liquid ice is on the picosecond time scale, 
and that of proton exchange in ice is on the millisecond time scale; the proton exchange rates in DNA and attached 
proteins may vary from picosecond to nanosecond, minutes or years, depending on the exact locations of the 
exchanged protons in the large biopolymers. 

A simple harmonic oscillator 'vibration' is only an oversimplified dynamic representation of the longitudinal 
vibrations of the DNA intertwined helices which were found to be anharmonic rather than harmonic as often 
assumed in quantum dynamic simulations of DNA. 







DNA Spacefilling molecular model 



DNA Dynamics 235 

Paracrystalline lattice models of B-DNA structures 

A paracrystalline lattice, or paracrystal, is a molecular or atomic lattice with significant amounts (e.g., larger than a 
few percent) of partial disordering of molecular arranegements. Limiting cases of the paracrystal model are 
nanostructures, such as glasses, liquids, etc., that may possess only local ordering and no global order. Liquid 
crystals also have paracrystalline rather than crystalline structures. 

Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which is a dynamic one in 

spite of the relatively rigid DNA double-helix stabilized by parallel hydrogen bonds between the nucleotide 

base-pairs in the two complementary, helical DNA chains (see figures). For simplicity most DNA molecular models 

ommit both water and ions dynamically bound to B-DNA, and are thus less useful for understanding the dynamic 

behaviors of B-DNA in vivo. The physical and mathematical analysis of X-ray and spectroscopic data for 

paracrystalline B-DNA is therefore much more complicated than that of crystalline, A-DNA X-ray diffraction 

patterns. The paracrystal model is also important for DNA technological applications such as DNA nano technology. 

Novel techniques that combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now 

also being developed (see, for example, 'Application of X-ray microscopy in the analysis of living hydrated cells" 
[15K 

Genomic and biotechnology applications of DNA molecular modeling 

There are various uses of DNA molecular modeling in Genomics and Biotechnology research applications, from 
DNA repair to PCR and DNA nanostructures. Two-dimensional DNA junction arrays have been visualized by 
Atomic force microscopy. 

Quadruplex DNA may be involved in certain cancers 

See also 

DNA structure 

X-ray scattering 

Neutron scattering 

Crystallography 

Crystal lattices 

2D-FT NMRI and Spectroscopy 

List of nucleic acid simulation software 

Sirius visualization software 

X-ray microscopy 

QMC@Home 

Sir Lawrence Bragg, FRS 

Spectroscopy 



FT-NMR [18] [19] 



Vibrational circular dichroism (VCD) 

• NMR Atlas-database [22] 

T231 

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data 

[24] 

• NMR constraints files for NAs in PDB format 

• NMR microscopy 

• Microwave spectroscopy 

• FT-IR 

• FT-NIR [21] [22] [23] 



DNA Dynamics 236 

c ♦ i tt * i a m, • i ■ • J 24 ! P5] [26] [21] [22] [27] [28] 

• Spectral, Hyperspectral, and Chemical imaging) 

[291 noi 

• Raman spectroscopy/microscopy and CARS 

• Fluorescence correlation spectroscopy , Fluorescence cross-correlation 

a cdctP 7 ] [38] [39] 

spectroscopy and FRET 

• Confocal microscopy 

Further reading 

• Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology .(June 2004) I. C. 
Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin., q-bio/0406047. 

• F. Bessel, Untersuchung des Theils der planetarischen Storungen, Berlin Abhandlungen (1824), article 14. 

• Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and Sons, Ltd., vols. 1 and 
2., 1966., 2024 pages. 

• Cantor, C. R. and Schimmel, P.R. Biophysical Chemistry, Parts I and II., San Franscisco: W.H. Freeman and Co. 
1980. 1,800 pages. 

• Voet, D. and J.G. Voet. Biochemistry, 2nd Edn., New York, Toronto, Singapore: John Wiley & Sons, Inc., 1995, 
ISBN0-471-58651-X., 1361 pages. 

• Watson, G. N. A Treatise on the Theory of Bessel Functions., (1995) Cambridge University Press. ISBN 
0-521-48391-3. 

• Watson, James D. Molecular Biology of the Gene. New York and Amsterdam: W.A. Benjamin, Inc. 1965., 494 
pages. 

• Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science, Inc. 2000. 

• Herbert R. Wilson, FRS. Diffraction of X-rays by proteins, Nucleic Acids and Viruses., London: Edward Arnold 
(Publishers) Ltd. 1966. 

• Kurt Wuthrich. NMR of Proteins and Nucleic Acids., New York, Brisbane,Chicester, Toronto, Singapore: J. 
Wiley & Sons. 1986., 292 pages. 

• Robinson, Bruche H.; Seeman, Nadrian C. (August 1987). "The Design of a Biochip: A Self-Assembling 
Molecular-Scale Memory Device". Protein Engineering 1 (4): 295-300. ISSN 0269-2139. Link [45] 

• Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson, Deborah Kuchnir & 
Winfree, Erik (22 December 2004). "Design and Characterization of Programmable DNA Nanotubes". Journal of 
the American Chemical Society 126 (50): 16344-16352. doi:10.1021/ja0443191. ISSN 0002-7863. 

• Keren, K; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun (November 2003). 
"DNA-Templated Carbon Nanotube Field-Effect Transistor" [46] . Science 302 (6549): 1380-1382. 

doi: 10. 1126/science. 1091022. ISSN 1095-9203. 

• Zheng, Jiwen; Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl, Richard A. & Seeman 
Nadrian C. (2006). "2D Nanoparticle Arrays Show the Organizational Power of Robust DNA Motifs". Nano 
Letters 6: 1502-1504. doi:10.1021/nl060994c. ISSN 1530-6984. 

• Cohen, Justin D.; Sadowski, John P.; Dervan, Peter B. (2007). "Addressing Single Molecules on DNA 
Nanostructures". Angewandte Chemie 46 (42): 7956-7959. doi:10.1002/anie.200702767. ISSN 0570-0833. 

• Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping; Ding, Baoquan; 
Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie & Seeman, Nadrian C. (2006). "Double 
cohesion in structural DNA nanotechnology". Organic and Biomolecular Chemistry 4: 3414—3419. 
doi:10.1039/b605212f. 

• Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic results 
and DNA sequence data". Bioinformatics 20: 3682—3686. 

• Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences". 
Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041 



DNA Dynamics 237 

External links 

• DNA the Double Helix Game From the official Nobel Prize web site 

• MDDNA: Structural Bioinformatics of DNA [47] 

• Double Helix 1953—2003 National Centre for Biotechnology Education 

• DNAlive: a web interface to compute DNA physical properties . Also allows cross-linking of the results with 

the UCSC Genome browser and DNA dynamics. 

[491 

• DiProDB: Dinucleotide Property Database . The database is designed to collect and analyse thermodynamic, 

structural and other dinucleotide properties. 

• Further details of mathematical and molecular analysis of DNA structure based on X-ray data 

• Bessel functions corresponding to Fourier transforms of atomic or molecular helices. 

• Application of X-ray microscopy in analysis of living hydrated cells 

T521 

• overview of STM/AFM/SNOM principles with educative videos 

Databases for DNA molecular models and sequences 
X-ray diffraction 

• NDB ID: UD0017 Database [17] 

• X-ray Atlas -database 

T541 

• PDB files of coordinates for nucleic acid structures from X-ray diffraction by NA (incl. DNA) crystals 

• Structure factors dowloadable files in CIF format 
Neutron scattering 



• ISIS neutron source: ISIS pulsed neutron source:A world centre for science with neutrons & muons at Harwell, 
near Oxford, UK. 

X-ray microscopy 

• Application of X 
Electron microscopy 

• DNA under electron microscope 



Application of X-ray microscopy in the analysis of living hydrated cells 



Genomic and structural databases 

— contains examples of base skews. 

[58] 



T571 
• CBS Genome Atlas Database — contains examples of base skews. 



• The Z curve database of genomes — a 3-dimensional visualization and analysis tool of genomes 

• DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids molecular structure models in 
PDB and CIF formats [59] 

Atomic force microscopy 

• How SPM Works [60] 

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [61] 



DNA Dynamics 238 

References 

[I] Franklin, R.E. and Gosling, R.G. recd.6 March 1953. Acta Cryst. (1953). 6, 673 The Structure of Sodium Thymonucleate Fibres I. The 
Influence of Water Content Acta Cryst. (1953). and 6, 678 The Structure of Sodium Thymonucleate Fibres II. The Cylindrically Symmetrical 
Patterson Function. 

[2] Cochran, W., Crick, F.H.C. and Vand V. 1952. The Structure of Synthetic Polypeptides. 1. The Transform of Atoms on a Helix. Acta Cryst. 

5(5):581-586. 
[3] Crick, F.H.C. 1953a. The Fourier Transform of a Coiled-Coil., Acta Crystallographica 6(8-9):685-689. 
[4] Watson, James D. and Francis H.C. Crick. A structure for Deoxyribose Nucleic Acid (http://www.nature.com/nature/dna50/watsoncrick. 

pdf) (PDF). Nature 171, 737-738, 25 April 1953. 
[5] Watson, J.D; Crick F.H.C. 1953b. The Structure of DNA., Cold Spring Harbor Symposia on Qunatitative Biology 18:123-131. 
[6] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953). "Molecular Structure of Deoxypentose Nucleic Acids" (http://www.nature.com/ 

nature/dna50/wilkins.pdf) (PDF). Nature 171 (4356): 738-740. doi:10.1038/171738a0. PMID 13054693. . 
[7] Elson D, Chargaff E (1952). "On the deoxyribonucleic acid content of sea urchin gametes". Experientia 8 (4): 143—145. 
[8] Chargaff E, Lipshitz R, Green C (1952). "Composition of the deoxypentose nucleic acids of four genera of sea-urchin". J Biol Chem 195 (1): 

155-160. PMID 14938364. 
[9] Chargaff E, Lipshitz R, Green C, Hodes ME (1951). "The composition of the deoxyribonucleic acid of salmon sperm". J Biol Chem 192 (1): 

223-230. PMID 14917668. 
[10] Chargaff E (195 1). "Some recent studies on the composition and structure of nucleic acids". J Cell Physiol Suppl 38 (Suppl). 

[II] Magasanik B, Vischer E, Doniger R, Elson D, Chargaff E (1950). "The separation and estimation of ribonucleotides in minute quantities". J 
Biol Chem 186 (1): 37-50. PMID 14778802. 

[12] Chargaff E (1950). "Chemical specificity of nucleic acids and mechanism of their enzymatic degradation". Experientia 6 (6): 201—209. 
[13] Hosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Pubis., Amsterdam — New York, 1962. 
[14] Baianu, I.C. (1978). "X-ray scattering by partially disordered membrane systems.". Acta Cryst., A34 (5): 751—753. 

doi: 10.1 107/S0567739478001540. 
[15] Mao, Chengde; Sun, Weiqiong & Seeman, Nadrian C. (16 June 1999). "Designed Two-Dimensional DNA Holliday Junction Arrays 

Visualized by Atomic Force Microscopy". Journal of the American Chemical Society 121 (23): 5437—5443. doi:10.1021/ja9900398. 

ISSN 0002-7863. 
[16] http://www.phy.cam.ac.uk/research/bss/molbiophysics.php 
[17] http://planetphysics.org/encyclopedia/TheoreticalBiophysics.html 

[18] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants 
[19] (http://www.spectroscopynow.com/FCKeditor/UserFiles/File/specNOW/HTML files/General_Karplus_Calculator.htm) Another 

Javascript-like NMR coupling constant to dihedral 
[20] Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213. 
[21] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High Resolution Nuclear Magnetic 

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis.,!). 

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL. 
[22] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy. 2004.1. 

C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006) 
[23] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY. 
[24] http://www.imaging.net/chemical-imaging/Chemical imaging 
[25] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining 

Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004. 
[26] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy., Microchimica Acta, 104, (1-6) 

January 1991, doi: 10.1007/BF01245536 
[27] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. Laboratory 

Journal Europe, No. 1-2, 2007. 
[28] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology. (June 2004)., I. C. Baianu, P. R. Lozano, V. I. 

Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047) 
[29] Chemical Imaging Without Dyeing (http://witec.de/en/download/Raman/ImagingMicroscopy04.pdf) 
[30] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine., 

doi: 10.1 146/annurev.anchem.l.031207. 112754 Annual Review of Analytical Chemistry, 1: 883-909. 
[31] Eigen, M., Rigler, R. Sorting single molecules: application to diagnostics and evolutionary biotechnology, (1994) Proc. Natl. Acad. Sci. USA, 

91,5740-5747. 
[32] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in biotechnology, (1995) J. 

Biotechnol., 41,177-186. 
[33] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy, BioScience (Ed. 

Klinge & Owman) p. 180. 



DNA Dynamics 239 

[34] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based amplification combined with 

fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281. 
[35] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of 

binary phospholipid mixtures. Biophys J., 78:290-305. 
[36] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by fluorescence correlation 

spectroscopy with one- and two-photon excitation. Biophysical Journal, 77(10):2251-2265. 
[37] FRET description (http://dwb.unl.edu/Teacher/NSF/C08/C08Links/pps99.cryst.bbk.ac.uk/projects/gmocz/fret.htm) 
[38] doi:10.1016/S0959-440X(00)00190-l (http://dx.doi.org/10.1016/S0959-440X(00)00190-l)Recent advances in FRET: distance 

determination in protein— DNA complexes. Current Opinion in Structural Biology 2001, 11(2), 201-207 
[39] http://www.fretimaging.org/mcnamaraintro.html FRET imaging introduction 



Interactomics 



Interactomics is a discipline at the intersection of bioinformatics and biology that deals with studying both the 
interactions and the consequences of those interactions between and among proteins, and other molecules within a 
cell . The network of all such interactions is called the Interactome. Interactomics thus aims to compare such 
networks of interactions (i.e., interactomes) between and within species in order to find how the traits of such 
networks are either preserved or varied. From a mathematical, or mathematical biology viewpoint an interactome 
network is a graph or a category representing the most important interactions pertinent to the normal physiological 
functions of a cell or organism. 

Interactomics is an example of "top-down" systems biology, which takes an overhead, as well as overall, view of a 
biosystem or organism. Large sets of genome-wide and proteomic data are collected, and correlations between 
different molecules are inferred. From the data new hypotheses are formulated about feedbacks between these 

[2] 

molecules. These hypotheses can then be tested by new experiments . 

Through the study of the interaction of all of the molecules in a cell the field looks to gain a deeper understanding of 
genome function and evolution than just examining an individual genome in isolation . Interactomics goes beyond 
cellular proteomics in that it not only attempts to characterize the interaction between proteins, but between all 
molecules in the cell. 

Methods of interactomics 

The study of the interactome requires the collection of large amounts of data by way of high throughput experiments. 
Through these experiments a large number of data points are collected from a single organism under a small number 

[2] 

of perturbations These experiments include: 

• Two-hybrid screening 

• Tandem Affinity Purification 

• X-ray tomography 

• Optical fluorescence microscopy 



Interactomics 



240 



Recent developments 

The field of interactomics is currently rapidly expanding and developing. While no biological interactomes have 
been fully characterized. Over 90% of proteins in Saccharomyces cerevisiae have been screened and their 
interactions characterized, making it the first interactome to be nearly fully specified 

Also there have been recent systematic attempts to explore the human interactome and 




Other species whose interactomes have been studied in some detail include Caenorhabditis elegans and Drosophila 
melanogaster. 



Criticisms and concerns 

Kiemer and Cesareni raise the following concerns with the current state of the field: 

• The experimental procedures associated with the field are error prone leading to "noisy results". This leads to 
30% of all reported interactions being artifacts. In fact, two groups using the same techniques on the same 
organism found less than 30% interactions in common. 

• Techniques may be biased, i.e. the technique determines which interactions are found. 

• Ineractomes are not nearly complete with perhaps the exception of S. cerivisiae. 

• While genomes are stable, interactomes may vary between tissues and developmental stages. 

• Genomics compares amino acids, and nucleotides which are in a sense unchangeable, but interactomics compares 
proteins and other molecules which are subject to mutation and evolution. 

• It is difficult to match evolutionary related proteins in distantly related species. 



Interactomics 24 1 

See also 

Interaction network 
Proteomics 
Metabolic network 
Metabolic network modelling 
Metabolic pathway 
Genomics 

Mathematical biology 
Systems biology 

External links 

• Interactomics.org . A dedicated interactomics web site operated under BioLicense. 

• Interactome.org . An interactome wiki site. 

[71 

• PSIbase Structural Interactome Map of all Proteins. 

ro] 

• Omics.org . An omics portal site that is openfree (under BioLicense) 

• Genomics.org .A Genomics wiki site. 

• Comparative Interactomics analysis of protein family interaction networks using PSIMAP (protein structural 
interactome map) 

• Interaction interfaces in proteins via the Voronoi diagram of atoms 

• Using convex hulls to extract interaction interfaces from known structures. Panos Dafas, Dan Bolser, Jacek 
Gomoluch, Jong Park, and Michael Schroeder. Bioinformatics 2004 20: 1486-1490. 

• PSIbase: a database of Protein Structural Interactome map (PSIMAP). Sungsam Gong, Giseok Yoon, Insoo Jang 
Bioinformatics 2005. 

• Mapping Protein Family Interactions : Intramolecular and Intermolecular Protein Family Interaction Repertoires 
in the PDB and Yeast, Jong Park, Michael Lappe & Sarah A. TeichmannJ.M.B (2001). 

ri2i 

• Semantic Systems Biology 

References 

[I] Kiemer, L; G Cesareni (2007). "Comparative interactomics: comparing apples and pears?". TRENDS in Biochemistry 25: 448—454. 
doi:10.1016/j.tibtech.2007.08.002. 

[2] Bruggeman, F J; H V Westerhoff (2006). "The nature of systems biology". TRENDS in Microbiology 15: 45—50. 

doi:10.1016/j.tim.2006.11.003. 
[3] Krogan, NJ; et al. (2006). "Global landscape of protein complexes in the yeast Saccharomyeses Cerivisiae ". Nature 440: 637—643. 

doi: 10.1038/nature04670. 
[4] further citation needed 
[5] http://interactomics.org 
[6] http://interactome.org 
[7] http://psibase.kobic.re.kr 
[8] http://omics.org 
[9] http://genomics.org 
[10] http://bioinformatics.oxfordjournals.org/cgi/content/full/21/15/3234 

[II] http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TYR-4KXVD30-2&_user=10&_coverDate=ll%2F30%2F2006& 
_rdoc=l&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=l&_urlVersion=0&_userid=10& 
md5=8361bf3fe7834b4642cdda3b979de8bb 

[12] http://www.semantic-systems-biology.org 



Article Sources and Contributors 242 

Article Sources and Contributors 

Spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=353906901 Contributors: 209.234.79. xxx, 5 albert square, ACrush, Aadal, Abdul wali98, AdjustShift, Adoniscik, Afrine, 
Ahmerpklll, Ahoerstemeier, Akhram, Al-khowarizmi, Alansohn, Andre Engels, Andycjp, Angry sockhop, Annabel, Aspiring chemist, Atlant, Austin512, Azo bob, Bci2, Beano, Becritical, 
BenFrantzDale, Bensaccount, Bj norge, Borgx, Bryan Derksen, Camw, CaneryMBurns, Charles Gaudette, Charles Matthews, Chemstry isMyLife, Christian List, Coffea, CommonsDelinker, 
Conversion script, Cortonin, Cremepuff222, Ctroy36, Curps, DMacks, DanskiI4, Deglr6328, Dekisugi, Dfbaum, Dicklyon, Dkroll2, Dpoduval, Dr-b-m, DrBob, Duncanssmith, Dysprosia, 
Edgarl81, El C, Eleassar, ErikvDijk, Erwinrossen, Fastfission, Femto, Flewis, FocalPoint, Fratrep, Fredericks, Fredrik, Frikensmurf, Gentgeen, Gerkleplex, Giftlite, Goldenrowley, Guillermo con 
sus ruedas, Gurch, H Padleckas, Hall Monitor, Hankwang, Harbir93, Harris7, Headbomb, Heron, Holdendp, Icairns, Ignoramibus, Ikanreed, IronGargoyle, J2thawiki, JNW, Jaeger5432, 
Jameswkb, Javert, Jcwf, JeremyA, JohnCD, Ken6en, Kevyn, Kilva, Kkmurray, Kopeliovich, Kraftlos, La Pianista, LeaveSleaves, Logger9, Marek69, Marj Tiefert, Martin Hedegaard, Martyjmch, 
Mav, MejorLos Indios, Melchoir, Michael Hardy, Mihano, Mikeo, Modlab, Mrs Trellis, Mtkl80, Mts0405, Nbkoneru, NicktaylorlOO, North Shoreman, Northryde, Nuno Tavares, Oxymoron83, 
PDManc, Pcarbonn, Pdcook, Peter, Petergans, Peterlewis, Pharmacomancer, Pit, Pizza Puzzle, Pjvpjv, Prgo, Prolog, Pyrospirit, Qxz, R'n'B, RG2, Radagast83, Ratsbew, Reddi, Renxa, Retired 
username, Rjwilmsi, Rnt20, RoadieRich, Rob Hooft, Rocoptics, Ronningt, RoyBoy, Rubin Joseph 10, Rvoorhees, S4wilson, Safalra, Sam Hocevar, Sbialkow, Scog, SemperBlotto, Shadowjams, 
Sharare, Shell Kinney, Shovskowska, Smack, Snags, Sodium, Srleffler, Srnec, StefanPl, Stone, StradivariusTV, T-borg, Taxman, Tegeasl7, Thelntersect, Thecurran91, Tibor Horvath, Tide rolls, 
Tim Starling, Tsemii, Tukan, Voyajer, Vsmith, Welsh, WiKi, Wik, Willi. am, Williamheyn, WinterSpw, Wk muriithi, Wpostma, Zereshk, Zotel, Zroutik, 304 anonymous edits 

Fourier transform spectroscopy Source: http://e11.wikipedia.0rg/w/index. php?oldid=353620276 Contributors: AJim, Asterion, Bci2, Bersbers, Berserkerus, BigFatBuddha, BobbylOl 1, 
Christopherlin, Conversion script, Damian Yerrick, Deglr6328, E104421, EndersJ, Epbrl23, Graeme Bartlett, Graham87, Greggklein, Guillom, Hankwang, Harold f, Haydarkustu, 
HelgeStenstrom, Jaraalbe, Jcwf, John.lindner, Jonathan F, Kcordina, Kingpinl3, Kkmurray, Martyjmch, Matanbz, Michael Hardy, Nikai, Nitrogenl5, PBSurf, Peter, Peterlewis, Publicly Visible, 
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Birefringence Source: http://en. wiki pedia.org/ w/index.php?oldid=35 377 3007 Contributors: A. B., Ackbeet, Avihu, Bluemoose, Brews ohare, Bryan Derksen, Catskul, Chocofever, Ciphers, 
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Polarization spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=336954I87 Contributors: Evgeny, Jovianeye, Rich257, ZooFari 

Polarized IR Spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=l 6987408 Contributors: 194.200. 130. xxx, Aboalbiss, Ahoerstemeier, Anna Lincoln, Annabel, Antandrus, 
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Tyciol, Tylerhammond2, Uirauna, Uncle Dick, User Al, Usmanmyname, VK3, VasilievVV, Vector Potential, Versus22, Voice of All, WLU, Wardface, WarthogDemon, Wayne Miller, 
Wayward, Whkoh, Wiki alf, Wikimercenary, WikipedianMarlith, WillowW, Wimt, Winchelsea, WinterSpw, Wisco, Wk muriithi, Wknight94, Wolfkeeper, Woohookitty, Work permit, 
Wuhwuzdat, Wwood, Xaosflux, Xavierschmit, Xelixed, Yamamoto Ichiro, Yanggers, Yidisheryid, Yurilinda, Yyy, Zafiroblue05, Zarius, Zenchu, Zephyris, Zoeiscow, ZooFari, Zsinj, Zzuuzz, 
1612 anonymous edits 

Protein structure Source: http://en.wikipedia.org/w/index.php?oldid=35446 1 300 Contributors: AC+79 3888, Abaighv, Ahoerstemeier, Akjohnson, Alan Au, Alansohn, Albval, Alchemist Jack, 
Anonymi, Antony-22, Apparitionl 1, Arcadian, AxelBoldt, Banus, BenolOOO, Berky, Biophys, Blueskylab, Bobol92, Can't sleep, clown will eat me, CardinalDan, Choij, Chris 73, Christopherlin, 
Chyrmera, Clicketyclack, Cmdrjameson, Cryptic C62, DVD R W, Dcrjsr, Debresser, DerHexer, Dmb000006, Elementl6, Elmer Clark, Enviroboy, Etxrge, Euchiasmus, Foolip, Friginator, Gaius 
Cornelius, Gene Nygaard, Ghakko, Gilliam, Graeme Bartlett, Grafened, Gurchzilla, Hbent, Ike9898, J.delanoy, JaGa, Janlnad, Jcwf, Jordell 000, K3rb, Kanonkas, Kjaergaard, Kochipoik, 
Konstantin, La Pianista, Law, Lexor, Loodog, Lynnbridgebook, Malenkylizards, Mandolinface, Math-ghamhainn, Michael A. White, Miguel Andrade, Mikelr, Moleculesoflife, Mushin, 
NeoJustin, Nina Gerlach, Nitya Dharma, Omicronpersei8, Opabinia regalis, P99am, Password, Pdcook, Phgao, Pinethicket, Pravinhiwale, Pro crast in a tor, Q31245, ROBE0191, Rasmusw, 
Recury, Retama, Rkirian, RyanGerbillO, Saganatsu, Seventy Three, Shadowjams, Shrimp wong, Sir Vicious, Sluzzelin, Smoe, Speedyboy, Splette, Stefano Garibaldi, Sverdrup, Team6and7, 
Theyeti, Thorwald, Tim Ross, TimVickers, TommymaclO, Tralala, Trusilver, Vijaykumarutkam, Vriend, Webridge, Wheedhee, WhinerOl, WillowW, Yamamoto Ichiro, 255 anonymous edits 

Protein folding Source: http://en.wikipedia.org/w/index.php'?oldid=35482791 8 Contributors: 168..., 5beta5, Adriferr, Agilemolecule, Akane700, Andraaide, Antony-22, Arcadian, Artoannila, 
Banus, Barticus88, Bci2, Bendzh, Bfinn, Bioinfol77, Biophys, Biophysik, Bkhouser, Blainster, Blooooo, BlurTento, Brianga, Bryan Derksen, Cacycle, Calvero JP, Cathalgarvey, Cburnett, 
ChicXulub, Clicketyclack, Computer, Cyberman, Czhangrice, D. Recorder, DannyWilde, Dave3457, Davepntr, DennisDaniels, Dhatz, Donarreiskoffer, Dwmyers, ESkog, Eequor, Erencexor, 
Erwinser, Fawzin, Fuzheado, Gcrossan, Gowantervo, Grimlock, Harley peters, Herd of Swine, Hooplehead, Intangir, Ixfd64, JJ TKOB, Jacobsman, Jammedshut, JeramieHicks, Katherine 
Folsom, Kevyn, Kierano, Kjaergaard, Konstantin, Kostmo, LarRan, Leptictidium, Lexor, Lfh, LiDaobing, Lir, Lostart, Lucaaah, M stone, Macintosh 10000, Madeleine Price Ball, Magnus 
Manske, Malcolm Farmer, Mark Renier, Michael Hardy, Miguel Andrade, Minghong, Mittinatten, MockAE, Movado73, Movalley, My very best wishes, Myscrnnm, Netesq, Opabinia regalis, 
Otvaltak, P99am, Piotrus, Pro crast in a tor, Ptrl23, RDBrown, Rebroad, Rich Farmbrough, Richyfp, Rjwilmsi, RoyBoy, RunninRiot, Samrat Mukhopadhyay, Sharkman, Shmedia, SirHaddock, 
Smelialichu, Snowmanradio, Splette, SpuriousQ, Stepa, Sunnyl7152, Taw, Terrace4, TestPilot, The Anome, The Great Cook, Tijmz, TimVickers, Tomixdf, Tommstein, Toytoy, Trenchcoatjedi, 
Trusilver, V8rik, Waerloeg, Wavelength, WillowW, WorldDownlnFire, Xnuala, Xy7, Yves-henri, Zoicon5, TWl, 168 anonymous edits 

Protein dynamics Source: http://en.wiki pedia.org/ w/index.php?oldid=290533592 Contributors: 168..., Abyzov, Altenmann, Anthony Appleyard, Bhadani, Biophys, Bulgaroctonus, 
CRGreathouse, Colonies Chris, Dejo, Dicky2206, Doopa, Elementl6, Flyguy649, Hoffmeier, Johnpseudo, Jvbishop, K.murphy, KestasUPSY, Loupeter, Mary Ann Summers, Mikael Haggstrom, 
MockAE, Nneonneo, Noalaignorancia, NuclearWarfare, P99am, Raffuzzo p, Rajah, RichardOOl , Sciencetalks, Sintaku, Someche, Substatique, Tameeria, Thorwald, Tibor Horvath, Timwi, 
Tnxman307, WhinerOl, Whosasking, Zashaw, 39 anonymous edits 

Nucleic Acids Source: http://en.wikipedia.org/w/index.php?oldid=20758770 Contributors: 168..., 2 of 8, A4, Abrech, Acelgoyobis, Adam Bishop, Addshore, Agathman, Alboyle, Alex43223, 
Alexius08, Anclation, Andre Engels, Angela, Anthere, Antony-22, Antzervos, Aoi, Arakunem, Araucaria, ArbitrarilyO, Babyranksl7, Barticus88, Beethoven's DNA, Beetstra, Bensaccount, 
Bobchicken9, Bobol92, Bradjamesbrown, CDN99, CL, CLW, Cacycle, Can't sleep, clown will eat me, Careless hx, Ceyockey, Chanoyu, ChaosR, ChrisCork, ChrisHodgesUK, Ciphers, 
Conversion script, Cpeditorial, Cyan, Daniel5127, DarkFalls, DerHexer, Desireader, Discospinster, Dng267, Dposse, Dungodung, Dysprosia, EconoPhysicist, Ed Poor, Ellmist, Emw, Forluvoft, 
Frankenpuppy, Franz Bryan, FreplySpang, G3pro, Gaia Octavia Agrippa, GeeJo, Gentgeen, Giftlite, Gilliam, Gogo Dodo, GraemeL, Graft, Grunty Thraveswain, Gurch, Gwernol, Hede2000, 
Hellow yo, Hellowhy, Hephaestos, Hu, Hydrogen Iodide, I dream of horses, It Is Me Here, J Di, J.delanoy, JForget, James086, Jhannah, Joanjoc, John R Murray, JonMoulton, Josh Cherry, Josh 
Grosse, K3f3rn, Kablammo, Kandar, Kbdank7I, Keegan, Kierano, KimvdLinde, Kkmurray, Kpjas, Kyle 290, LAX, La goutte de pluie, Laurascudder, Leonard Vertighel, Lexor, Liamdaly620, 
Lir, Looie496, Luna Santin, LyXX, M80forYOU, Magog the Ogre 2, Marudubshinki, Mav, Maxxicum, Mendaliv, Miaow Miaow, Mikegrant, Miszal3, Mlouns, Mygerardromance, Narayanese, 
Narsil, Ngourlie, Nk, Nposs, NuclearWarfare, Omicronpersei8, Onco p53, OrangeDog, Oxymoron83, P99am, Pakaran, Pgan002, Pharaoh of the Wizards, Philip Trueman, Piano non troppo, 
Pobregatita, Possum, Ppgardne, Ppntori, Preston. hussey, Pschemp, RJaguar3, Rcej, Res22 1 6firestar, Rifleman 82, SJP, Scharks, Schmutz MDPI, Sciurinae, Seba5618, Sgpsaros, ShellCoder, 
Silsor, Simeon H, Sintaku, SixPurpleFish, Smack, Smaugl23, Snoyes, Squidonius, Stephen5406, Stewartadcock, Strl977, Strathallen, Tad Lincoln, Talon Artaine, TheTito, Thehelpfulone, 
Thingg, Tide rolls, Timl357, TimVickers, TimonyCrickets, Trevor Maclnnis, Tuganax, U.S.A.U.S.A.U.S.A., Ugen64, Uncle Dick, User Al, VIOLENTRULER, Vary, Versus22, Violetriga, 
W3bj3dl, Waggers, Wikipedia addictlOl, Wimt, Wisdom89, Wysprgr2005, Xdenizen, Yachtsmanl, Yk Yk Yk, Ziusudra, 488 anonymous edits 

DNA Source: http://en.wikipedia.Org/w/index. php?o!did=35 5095 288 Contributors: (, (jarbarf), -Majestic-, 168.., 168..., 169, 17Drew, 3dscience, 4ule, 62.253.64.xxx, 7434be, 84user, A D 13, A 
bit iffy, A-giau, Aaaxlp, Aatomicl, Academic Challenger, Acer, Adam Bishop, Adambiswangerl , Adamstevenson, Adashiel, Adenosine, Adrian. benko, Ahoerstemeier, Aitias, AJ123456, Alai : 
Alan Au, Aldaron, Aldie, Alegoo92, Alexandremas, Alkivar, Alphachimp, Alzhaid, Amboo85, Anarchy on DNA, Ancheta Wis, AndonicO, Andre Engels, Andrew wilson, Andreww, Andrij 
Kursetsky, Andycjp, AnitaI988, Anomalocaris, Antandrus, Ante Aikio, Anthere, Anthony, Anthony Appleyard, Antilived, Antony-22, Aquaplus, Aquilla34, ArazZeynili, Arcadian, Ardyn, 
ArielGoId, Armored Ear, Artichoker, Asbestos, Astrowob, Atlant, Aude, Autonova, Avala, AxelBoldt, AySz88, AzaToth, B, BD2412, BMF81, Banus, BaronLarf, Bbatsell, Bci2, Bcorr, Ben 
Webber, Ben-Zin, BenBildstein, Bender235, Benjah-bmm27, Bensaccount, Bernie Sanders' DNA, Bevo, Bhadani, BharlOOlOl, BiH, Bijee, BikA06, Bill Nelson's DNA, Billmcgnl89, Biolinker, 
Biriwilg, Bjwebb, Bkell, Blastwizard, Bloger, Blondtraillite, Bmtbomb, Bobblewik, Bobol92, Bongwarrior, Borisblue, Bornhj, Brian0918, Brighterorange, Briland, Brim, Brockett, Bryan, Bryan 
Derksen, CWY2190, Cacycle, Caerwine, Cainer91, Cal 1234, Calaschysm, Can't sleep, clown will eat me, Canadaduane, Carbon-I6, Carcharoth, Carlo.milanesi, Carlwev, Casliber, Cathalgarvey, 
CatherineMunro, CattleGirl, Causa sui, Cburnett, Cerberus lord, Chanora, Chanting Fox, Chaojoker, Charm, Chill Pill Bill, Chino, Chodges, Chris 73, Chris84, Chuck Grassley's DNA, Chuck02, 
Clivedelmonte, ClockworkSoul, CloudNine, Collins. mc, Colorajo, CommonsDelinker, Conversion script, Cool3, Coolawesome, Coredesat, Cornacchial23, Cosmotron, Cradleloverl23, 
Crazycomputers, Crowstar, Crusadeonilliteracy, CryptoDerk, Crzrussian, Cubskrazy29, CupOBeans, Curehd, Curps, Cyan, Cyclonenim, Cyrius, D6, DIREKTOR, DJAX, DJRafe, DNA EDIT 
WAR, DNA is shyt, DVD R W, Daniel Olsen, Daniel987600, Danielkueh, Danny, Danny B-), Danskil4, Darklilac, Darth Panda, Davegrupp, David D., David Eppstein, Davidbspalding, Daycd, 
Db099221, Dbabbitt, Dcoetzee, DeAceShooter, DeadEyeArrow, Delldot, Delta G, Deltabeignet, DevastatorllC, Diberri, Dicklyon, Digger3000, Digitalme, Dina, Djml279, Dlohcierekim's sock, 
Dmn, DocWatson42, Docjames, Doctor Faust, Docu, Dogposter, DonSiano, Donarreiskoffer, Dr dl2, Dr.Kerr, Drini, Dudewheresmywallet, Dullhunk, Duncan. france, Dungodung. 
Dysmorodrepanis, E. Wayne, ERcheck, ESkog, Echo parkOO, Echuck215, Eddycrai, Editing DNA, Edwy, Efbfweborg, Egil, ElTyrant, Elb2000, Eleassar777, EliasAlucard, ElinorD, Ellmist, 
Eloquence, Emoticon, Emw, Ephemeronium, Epingchris, Erik Zachte, Escape Artist Swyer, Esurnir, Etanol, Ettrig, EurekaLott, Everyking, Evil Monkey, Ewawer, Execvator, FOTEMEH, 
Fabhcun, Factual, Fagstein, Fastfission, Fconaway, Fcrick, Fernando S. Aldado, Ffirehorse, Figma, Figure, Firetrap9254, Fishingpal99, Flavaflavl005, Florentino floro, Fnielsen, Forluvoft, 
Freakof nurture, FreplySpang, Friendly Neighbour, Frostyservant, Fruge, Fs, Fvasconcellos, G3pro, GAThrawn22, GHe, GODhack, Gaara san, Galoubet, Gary King, Gatortpk, Gazibara, GeeJo, 
Gene Nygaard, GeoMor, Giftlite, Gilisa, Gilliam, Gimmetrow, Gjuggler, Glen Hunt's DNA, Glenn, Gmaxwell, GoEThe, Goatasaur, Gogo Dodo, Golnazfotohabadi, GordonWatts, Gracenotes, 
Graeme Bartlett, GraemeL, Grafikm fr, Graft, Graham87, GrahamColm, Grandegrandegrande, GregorB, Grover Cleveland, Gurko, Gustav von Humpelschmumpel, Gutza, Gwsrinme, Hadal, 
Hagerman, Hairchrm, Hairwheel, Hammersoft, Hannes Rost, Harianto, HayleyJohnson2 1 , Heathhunnicutt, Hephaestos, Heron, Heyheyhack, Hockey21dude, Horatio, Hu, Hughdbrown, 
Hurricanehink, Hut 8.5, Hvn0413, I hate DNA, Iapetus, Icairns, Ilia Kr., Impamiizgraa, InShaneee, Inge-Lyubov, Isilanes, Isis07, Itub, Ixfd64, Izehar, JHMM13, JWSchmidt, JWSurf, Jacek 
Kendysz, Jackrm, JamesMLane, JamesMtl984, Janejellyroll, Javert, Jaxl, Jeka911, Jerome, JeremyA, Jerzy, Jetsetpainter, Jh51681, Jiddisch, Jimriz, Jimwong, Jlh29, Jls043, Jmccl50, Jo9100, 
JoanneB, Joconnol, Joeywallace9, Johanvs, JohnArmagh, Johntex, Johnuniq, Jojit fb, JonMoulton, Jonrunles, Jonverve, Jorvik, JoshuaZ, Josq, Jossi, Jstech, Julian Diamond, Jumbo Snails, Junes, 
Jwrosenzweig, Kahlfin, Kapow, Karrmann, Kazkaskazkasako, Kbh3rd, Keegan, Keepweek, Keilana, Kelly Martin, Kemyou, Kendrick7, Kerry077, Kevin B12, Kevmitch, Kghose, Kholdstare99, 
Kierano, KimvdLinde, King of Hearts, KingTT, Kingturtle, Kitch, Knowledge Seeker, KnowledgeOfSelf, Koavf, KrakatoaKatie, Kums, Kungfuadam, Kuru, Kwamikagami, Kwekubo, KyNephi, 
LA2, LFaraone, La goutte de pluie, Lascorz, Latka, Lavateraguy, Lee Daniel Crocker, Lemchesvej, Leptictidium, Lerdsuwa, Leuko, Lexor, Lhenslee, Lia Todua, LightFlare, Lightmouse, 
Lightspeedchick, Ligulem, Lincher, Lion Wilson, Lir, Llongland, Llull, Lockesdonkey, Logical2u, Loginbuddy, Looxix, Loren36, Loris, Luigi30, Luk, Lumos3, Luna Santin, Luuva, MER-C, 
MKoltnow, MONGO, Mac, Madeleine Price Ball, Madhero88, Magadan, Magnus Manske, Majorly, Malcolm rowe, Malo, Mandyj61596, Mantissal28, Marcus.aerlous, Marj Tiefert, 
Martin.Budden, MarvPaule, Master dingley, Mattbr, Mattbrundage, Mattjblythe, Maurice Carbonaro, Mav, Max Baucus' DNA, Max Naylor, McDogm, Medessec, Medos2, Melaen, Melchoir, 
Mentalmaniac07, Mgiganteusl, Mgtoohey, Mhking, Michael Devore, MichaelHa, MichaelaslO, Michigan user, MidgleyDJ, Midnightblueowl, Midoriko, Mika293, Mike Rosoft, Mikker, Mikko 
Paananen, Mintmanl6, MisfitToys, Miszal3, Mithent, Mjpieters, Mleefs7, Moink, Moorice, Mortene, Mr Bungle, Mr Meow Meow, Mr Stephen, MrErku, Mstislavl, Mstroeck, Mulad, Munita 
Prasad, Muro de Aguas, Mwanner, Mxn, Nakon, Narayanese, Natalie Erin, Natarajanganesan, Natel028, NatureA16, Nauseam, Nbauman, Neckro, Netkinetic, Netoholic, Neutrality, Never give 
in, NewEnglandYankee, Nighthawk380, NighthawkJ, Nihiltres, Nirajrm, Nishkid64, Nitecrawler, Nitramrekcap, No Guru, NoIdeaNick, NochnoiDozor, Nohat, Northfox, NorwegianBlue, 
Nthornberry, Nunh-huh, OBloodyHell, OOODDD, Obli, Oblivious, Ocolon, Ojl, Omicronpersei8, Onco p53, Opabinia regalis, Opelio, Orrin Hatch's DNA, Orthologist, Ortolan88, Ouishoebean, 
Outriggr, OwenX, P99am, PDH, PFHLai, PaePae, Pakaran, Pascal666, PatrickOMoran, Patrick2480, Patstuart, Paul Foxworthy, Paul venter, Paulinho28, Pcb21, Pde, Peak, Pedro, Persian Poet 
Gal, Peter Isotalo, Peter K., Peter Winnberg, Pgan002, Philip Trueman, PhilipO, Phoenix Hacker, Pierceno, PierreAbbat, Pigman, Pigmietheclub, Pilotguy, Pkirlin, Poor Yorick, Portugue6927, 



Article Sources and Contributors 246 

Potatoswatter, Preston47, Priscilla 95925, Pristontalel 1 1, Pro crast in a tor, Prodego, Psora, PsyMar, Psymier, Pumpkingrower05, Pyrospirit, Quebec99, Quickbeam, Qutezuce, Qxz, R'n'B, R. S. 
Shaw, RDBrown, RJC, RSido, Ragesoss, Rajwikil23, RandomP, Randomblue, Raul654, Raven in Orbit, Ravidreams, Rdb, Rdsmith4, Red Director, Reddi, Rednblu, Redneckjimmy, Redquark, 
Retired username, Rettetast, RexNL, Rich Farmbrough, RichG, Richard Durbin's DNA, Ricky81682, Rjwilmsi, Roadnottaken, Robdurbar, RobertG, Rocastelo, RoddyYoung, Rory096, Rotem 
Dan, Roy Brumback, RoyBoy, RoyLaurie, Royalguardl 1, RunOrDie, Russ47025, RxS, RyanGerbillO, Ryulong, S77914767, SCEhardt, STAN SWANSON, SWAdair, Sabbre, Safwan40, 
Sakkura, SallyForthl23, Sam Burne James, Samsara, Samuel, Samuel Blanning, SandyGeorgia, Sangol23, Sangwine, Savidan, Scarce, Sceptre, Schutz, Sciencechick, Sciencemanl23, 
Scincesociety, Sciurime, Scope creep, Scoterican, Sean William, SeanMack, Seans Potato Business, SebastianHawes, Seldonl, SemperBlotto, Sentausa, Serephine, Shadowlynk, Shanes, ShaunL, 
Shekharsuman, Shizhao, Shmee47, Shoy, Silsor, SimonD, Sintaku, Sir.Loin, Sjjupadhyay, Sjollema, Sloth monkey, Slrubenstein, Sly G, SmilesALot, Smithbrenon, Snowmanradio, Snowolf, 
Snurks, Solipsist, Someone else, Sonett72, Sopoforic, Spaully, Spectrogram, Spiff, Splette, Spondoolicks, Spongebobsqpants, SpuriousQ, Squidonius, SquirepantslOl, Statsone, Steel, Steinsky, 
Stemonitis, Stephenb, SteveHopson, Stevertigo, Stevietheman, Stewartadcock, Stuart7m, Stuhacking, SupaStarGirl, Supspirit, Susvolans, Sverdrup, Swid, Switchercat, Taco325i, Takometer, 
TakuyaMurata, Tariqabjotu, Tarret, Taulant23, Tavilis, Tazmaniacs, Ted Longstaffe, Tellyaddict, TenOfAUTrades, Terraguy, TestlOOOOO, TestPilot, The Rambling Man, The WikiWhippet, 
TheAlphaWolf, TheChrisD, TheGrza, TheKMan, TheRanger, Thorwald, ThreeDaysGraceFanlOl, Thue, Tiddly Tom, Tide rolls, TigerShark, TimVickers, Timewatcher, Timir2, Timl2k4, 
Timrollpickering, Timwi, Tobogganoggin, Toby Battels, TobyWilsonl992, Tom Allen, Tom Harkin's DNA, Tomgally, Toninu, Tonyl, Tonyrenploki, Trd300gt, Trent Lott's DNA, Triwbe, 
Troels Arvin, Tstrobaugh, Tufflaw, Turnstep, Twilight Realm, Tyl46Tyl46, UBeR, Unint, Unukorno, Usergreatpower, Utcursch, Uthbrian, Vaernnond, Vandelizer, Vanished user. Vary, 
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ZScout370, Zahid Abdassabur, Zahiri, Zanaq, Zazou, Zell Miller's DNA, Zephyris, Zoicon5, Zouavman Le Zouave, Zsinj, Zven, 1329 anonymous edits 

Molecular models of DNA Source: http://en.wikipedia.org/w/index.php'?oldid=354145216 Contributors: Antony-22, Bci2, Chris the speller, CommonsDelinker, David Eppstein, Jwoodger, 
Michael Hardy, Miym, Nmedard, Oscarthecat, P99am, Tassedethe, The Thing That Should Not Be, 2 anonymous edits 

DNA structure Source: http://en.wikipedia.org/w/index.php?oldid=354836243 Contributors: Andreww, Antandrus, Bci2, CDN99, Chodges, Cybercobra, DVD R W, DabMachine, David 
Eppstein, Dysmorodrepanis, Forluvoft, Gene Nygaard, Hannes Rost, Harold f, Joel7687, John Vandenberg, Josq, Leptictidium, Livingrm, Lockesdonkey, Luuva, Maikfr, Mr.Z-man, MrHaiku, 
Nasz, P99am, PatrickOMoran, Pinethicket, Rajan.kartik, Reinyday, Rich Farmbrough, Simulations, SuperHamster, Thorwald, TimVickers, Tomgally, Wknight94, Yahel Guhan, Yworo, Zephyris, 
40 anonymous edits 

DNA Dynamics Source: http://en.wikipedia.org/w/index.php?oldid=348694079 Contributors: Antony-22, Bci2, Chris the speller, CommonsDelinker, David Eppstein, Jwoodger, Michael Hardy, 
Miym, Nmedard, Oscarthecat, P99am, Tassedethe, The Thing That Should Not Be, 2 anonymous edits 

Interactomics Source: http://en.wikipedia.org/w/index.php?oldid=326148707 Contributors: Bci2, Bdevrees, Erick.Antezana, Erodium, J04n, Jong, Jongbhak, Karthik.raman, Lexor, Llull, 
Niteowlneils, PDH, Pekaje, Rajah, Tucsontt, 8 anonymous edits 



Image Sources, Licenses and Contributors 247 

Image Sources, Licenses and Contributors 

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Dbenbenn, Ejdzej, Falcorian, Kborland, MichaelDiederich, Mion, Saperaud, 6 anonymous edits 

File:QuantumDot wf.gif Source: http://en.wikipedia.org/w/index.php?title=File:QuantumDot_wf.gif License: Public Domain Contributors: Saumitra R Mehrotra & Gerhard Klimeck 
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Image:c60 isosurface.png Source: http: //en. wikipedia. org/ w/index.php?title=File:C60_iso surf ace. png License: GNU Free Documentation License Contributors: Usenltamblyn 
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Wutsje, 5 anonymous edits 

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Image: Asymmetrical stretching.gif Source: http://en.wikipedia.org/w/index.php?title=File:AsymmetricaI_stretching.gif License: Public Domain Contributors: Tiago Becerra Paolini 
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